I thought I'd write up kind of a basic primer for people who are playing this game for the first time.
The most important shortcut/thing to know is that you can right click on things to find out what they are. It shows you what a building or unit does, what some object on the map is, and lets you evaluate the strength of random units on the map by showing you how many enemies there are (in rough terms).
HOW TO PLAY
Before the game begins, you must choose a starting town type and starting hero. You can right click the types/heroes to see a little information, but here's a basic overview.
Castle: Medieval army-type units like swordsmen and archers with the addition of gryphons and angels at high levels. Good, balanced town type with strong units and average magic.
Rampart: Fairy-kingdom units like elves, unicorns, and treants, as well as powerful dragons. Most units are slow but strong, above-average magic.
Tower: Wizard's castles with units like gargoyles, golems, genies, and giants. Expensive units, but the high-end units are very powerful. Very good magic.
Dungeon: Creatures of the underground like troglodytes, minotaurs, medusas, and some dragons. Good ranged attackers, fairly expensive (but strong) units overall and very good magic.
Inferno: Hell-spawned demon units. Most units are relatively inexpensive but are fairly weak. Decent magic, typically gets very destructive spells.
Necropolis: Undead. Heroes have the necromancy skill, which raises the fallen as skeletons to serve your army. Short on ranged firepower, but the middle-ground units have very useful special abilities (like vampire lords).
Very good magic.
Stronghold: Barbarians with goblins, wargs, cyclopes, ogres, etc. Very high attack but low-ish defense. Poor magic.
Fortress: Swamp creatures like lizardmen, basilisks, and hydras. Units are inexpensive but fairly weak, though they have some interesting special abilities. Poor magic.
Conflux: Elementals of all types. Can build a lot of mid-power units, but don't have any extremely strong units like the archangels or dragons. Heroes have very good magic ability, probably the best of all the town types.
Each hero has a specialization, either a creature type, skill, or spell. Creature type heroes make a specific creatur stronger. Skill heroes are particularly good at a certain skill and the bonuses get better at higher levels. Spell heroes get extra efficacy out of a specific spell (and start with it, even if it's a high level spell like inferno or chain lightning).
You start most maps with one town (chosen before the game) and one hero. The tutorial explains this part, but you click your hero to select him or her, then click the place where you want to move; you'll see a path. Clicking again makes the hero move along the path. If you move into an object or creature (you'll see a sword icon) you'll pick it up or engage in combat. If you move onto a mine or other overworld map building, you'll claim it or activate it. You can also select a hero by clicking his portrait in the sidebar; clicking an already selected hero will show you a menu with the hero's stats, skills, artifacts, spellbook, and troops.
Exploring the map is a big part of Heroes 3. There's no fog of war, so any area you explore is (usually) permanently revealed. As you move your hero around the map, you'll find loose resources to grab, mines that increase your income in specific resources, and miscellaneous buildings that have various effects; for example, moving a hero onto a Mercenary's Camp permanently increases his attack score by 1.
You can see a town by either clicking it on the map or clicking the town's icon in the sidebar. Once you're at the "town screen," you can click the town hall structure (hovering over buildings tells you what they are) to bring up the build menu, or you can select and use other town structures by clicking on them. If you hold right-click on a town structure in the build menu, the game will tell you what it does and how much it costs. You can click the structure and your loyal followers will build it for you.
You can only build one building per day in a given town.
HEROES
Heroes do not participate in combat directly, but you can't have units wandering the map without a hero to lead them, so heroes are very important. Heroes can also cast spells, and their stats increase the stats of their units. Each hero has four stats: Attack Skill, Defense Skill, Power, and Knowledge. Each town type has a "Might" hero and a "Magic" hero. The Might heroes typically have better Attack and Defense, and do not start will spellbooks. Magic heroes are the opposite, having good Power and Knowledge.
Attack and Defense Skill add to the offense and defense of units under the hero's command. Power makes spells deal more damage and have increased duration. Knowledge determines hero max spell points. When a hero gains a level, he will get a stat boost in one of these four areas at random, with his class determining the probability of each increase.
Heroes have "secondary skills" like ballistics, archery, or wisdom that they gain as they level. Each level gives your hero a chance to learn or improve one skill; you're given a choice between two skills when you level. A hero can only learn eight different skills. Each skill gives your hero the ability to do something special, such as a bonus to ranged attack units, improved spellcasting, or increased movement. Choose wisely based on the kind of hero you want to create and on the kinds of skills that will most benefit your units (archery is worthless without ranged attackers, for example).
TOWNS
Town structures can be divided into two general categories: Creature dwellings and other structures. Every town has seven different creature dwellings (each with an upgraded version). At the beginning of each game week, creatures will spawn in the dwellings (in numbers indicated by their growth rate, which you can check in the bottom left of the town screen or at the castle). The other structures in each town have various benefits, like increasing creature growth rate or boosting hero stats.
There are five structures that every town, regardless of alignment, has access to. These are the town hall, castle, marketplace, blacksmith, and mage guild.
Town Hall: The more-upgraded your town hall is, the more gold you get each turn for owning the town. There are four levels of upgrade, earning you 500, 1000, 2000, or 4000 gold each turn.
Castle: The more-upgraded your castle is, the more creatures your dwellings will spawn each week. The castle also helps you defend your town when you are under attack by creating defenses, such as walls, arrow towers, and a moat.
Marketplace: Allows you to trade resources for other resources.
Blacksmith: Lets you build some kind of war machine specific to your town. Ballistae are ranged attack units, first aid tents heal your units, and ammo carts give your ranged attackers infinite ammo. Ballistae and first aid tents are basically useless unless you have heroes with skills relating to their use (ballistics and first aid), and a ballista is useless if the hero does not have a high attack score.
Mage Guild: Built from levels 1 to 5, the mage guild teaches spells to your hero and allows non-caster heroes to buy a spellbook so that they can learn spells. It also regenerates the spell points of a visiting hero; normally, spell points regenerate at only a very slow rate.
Most buildings have prerequisites. You need to build a blacksmith, marketplace, and mage guild before you can build the city hall (level 3 town hall building), for example.
UNITS AND COMBAT
The most important thing to remember about Heroes 3 is that individual units aren't worth much. You don't command a small group of units and individually move them; you command "stacks" of units. One pikeman is worthless, but a "stack" of 400 pikeman is kinda dangerous. The entire stack moves together as a single unit, but the damage of the whole stack is summed when attacking. When a stack takes damage, the first unit on the stack recieves the damage. If that unit is killed, the damage spills over to the next unit on the stack, and so on. A strong attack may kill hundreds of units on a single stack in a single blow. You don't have to stack all units of the same type together if you don't want to; for example, you might create multiple stacks of master genies because each stack can cast a beneficial spell on allies three times per battle, and if you make individual stacks you can use the ability more frequently. Usually, it's a good idea to stack similar units together, but there are exceptions.
A hero can carry at most 7 stacks of creatures in his army.
Combat takes place on a big hex grid. I recommend going to options and setting "show grid" and the other options like "cursor shadow" and "movement shadow" to on so that you can see the grid and how far your creatures can move on it without having to manually count hexes. Creatures move in order based on their speed and a creature stack can move as far as its speed in hexes. Once every creature on the battlefield has moved, the next round begins. You can choose to "wait" (click the hourglass) to delay a creature's turn until all other creatures have moved, or you can click "defend" (the shield) to give the creature a defense bonus without moving it.
Ranged attackers suffer a penalty (in most cases) if the target is over half the screen away or they are shooting over a castle wall. Ranged creatures also suffer a penalty for attacking at melee range (normally).
If a creature stack is attacked in melee, it typically gets one counterattack per round; the second time it is attacked in the same round, it gets no counterattack. This means that when attacking a strong creature creature, it is sometimes best to have a stack that will survive the counterattack strike first to deny the stack a counterattack so that the counterattack doesn't totally destroy a weaker stack. Some creatures deny counterattacking or get multiple counterattacks.
Creatures also have morale and luck. You get morale bonuses for having all of one town type of units in your army and take a penalty for mixing town types (a castle pikeman, rampart elf, and inferno imp stack in your army would penalize them all). If you have good morale, your units sometimes get double actions in combat. Bad morale causes your creatures to freeze occasionally and lose their turn. Morale can also be increased by artifacts and the hero leadership skill. Luck allows your creatures to have a chance to deal double damage when attacking. You can't have bad luck; it is increased by artifacts or the luck skill. Both morale and luck are rated from -3 to +3, with 0 being the norm.
Heroes can participate in the battle by casting one spell per round (as long as they have spell points). Spells can buff creature stacks, weaken creature stacks, create obstacles, or deal direct damage. As always, you can right click a spell in your spellbook to see what it does.
BASIC STRATEGY
Every week, you get more creatures you can purchase (they "grow" at the buildings in your town). You can only build one building per day, and your income is determined by your having mines or town buildings. Because of the limitations on building one structure per day, the first week is very strategically important. Generally, there are two different directions you can go the first week: You can try to maximize your income or you can maximize your army.
One route you can take is to upgrade that structure as fast as possible (so you have to build the mage guild, blacksmith, and marketplace first) so that you can have maximum gold. Once you have a capitol and are getting 4,000 gp daily from it, you start building creature dwellings.
The other strategy is to build as many creature dwellings and or the highest level fort/castle you can by the end of week one, which means you'll have maximum creatures to recruit at the beginning of the second week. However, you may not be able to afford them, so at that point you shift over to trying to increase your gold upkeep. This works better if there are a lot of resources and treasure for you to grab with your heroes around the starting point.
Because exploration of the map is so important, I usually hire multiple heroes on the first day so that I have three or four of them. Not all of them need to have a significant army if there're "unguarded" resources and stuff for you snag, and they can just scout for you.
A big part of the game is learning how to judge the strength of enemy units and monster groups; you can right click on just about anything to see what it is. The game will tell you in vague terms how strong the group is; for example, "lots of gremlins" or "a throng of pixies."
Few: 1-4
Several: 5-9
Pack: 10-19
Lots: 20-49
Horde: 50-99
Throng: 100-249
Swarm: 250-499
Zounds: 500-999
Legion: >1000
Numbers aren't everything; a throng of troglodytes is no problem if you have magic or ranged attackers to chip away at them before they even reach your units, but even a few black dragons can be trouble for an unprepared army.
Edit: Some good guides/tip stuff I've found on the web.
http://www.gamespot.com/features/heroesiii_gg/
http://www.heroesofmightandmagic.com/he ... 3iii.shtml