These are good general strategy tips to use when playing Heroes of Might and Magic.

• Artifacts and treasures are often hidden behind trees and mountains, etc. You can't see them, but the computer can! To grab the goodies before the computer does, place the horse icon somewhere, and if it turns to a rearing horse icon, there's something to be had! This applies to any map location where you can do something.
• If you try to grab an artifact lying on the ground, you may have to pay for it. If you can't afford it, then say yes anyway, and the seller will refuse to sell it. The artifact will still be there next turn when you have the cash. However, if you say no, the artifact disappears and is gone forever.
• Never spread your forces too thin among many heroes. Build up 2 "super" heroes, one to protect your castle, and the other to go around conquering. You can have extra heroes as scouts, however. They can just go around grabbing resources and mines. Another note is to never let your castle hero go further than one turn's travel from your castle, or you may lose it.
• Always save your game before starting a battle, no matter how sure a win it may seem. You may want to reload and see if you can do it faster, or with fewer losses, or not do it at all.
• Never use the AutoBattle option! The computer just wastes your spells, and has your troops do crazy things.
• A good way to be sure you will be able to hire troops immediately after capturing a castle, do it on day 7, so you should be able to hire troops the next day (unless it's Week of the PLAGUE!).
• If you want to try to reduce the enemy's finances, capture one of its' castles. Hire all the troops available, and leave right away. The enemy will recapture the castle, then split up it's army to leave a garrison to protect it. The castle should be easy to recapture to do it again, or the hero could be weakened enough to bump him off ;-) This is also a good trick to weaken a strong hero!
• Once in a while, you should check the hero pool in your castle to see if there are any good heroes available for hire. You may get lucky and get to hire a hero with an artifact or two!
• The above tip reminds me of another similar one I use when in battle. If you are fighting a strong hero you can't beat, and you want to keep your hero's artifacts, or his army, simply surrender if you can. Next turn, go into one of your castles and rehire him (with his army and artifacts!) for just 2500! To learn more about surrendering, visit the General Information Section.
• At the beginning of the game, hire a couple extra heroes as scouts. Get Barbarians for their movement bonus, and/or Warlocks for their larger search radius. These guys should avoid battles (unless against Peasants, or if you have shooters) and run around grabbing resources and mines. Don't worry about losing them too much, since they're just throwaway heroes.
• I like to call this a kamikaze attack (or hit and fade, or strike and return). Let's say there's a strong hero heading for your castle, and your strong heroes are elsewhere, or you don't think you can beat him. In your castle, hire a throwaway hero with a high spell power and the Armageddon spell. Put a couple of fast troops in his army (so you can hopefully go first), and go meet the impending danger. Right away, cast Armageddon. You will probably be wiped out from the blast, but your enemy should have been damaged also. Cast Armageddon again if you can, or retreat/surrender. Without ending your turn, go into your castle again and hire another throwaway hero (or the first one if you surrendered) and do it again and again, until you can't afford to hire any more heroes, or you think the enemy is sufficiently weakened to defeat with your regular army. Obviously, this won't be totally effective if your enemy has Dragons in his army, so you may need to fight the enemy anyway. Another note is that Warlocks are usually better for this maneuver, since they have a higher spell power at level 1 anyway, and they tend to grow stronger in that area.
• If you have shooters (Elves, Druids, Centaurs, Archers, Orcs) in your army when attacking a castle, the garrison (the one that shoots from the tower) usually makes short work of them, unless your hero has a high defense skill. There is some hope for the Trolls though. They have 40 HP, and the tower usually does about 40 damage. So cast Protection on the Trolls, and they should all survive the tower's shot. And the nifty thing is, the Trolls regenerate lost HP at the beginning of another round! So they can go on almost indefinitely, as long as their defense is high. Of course, this may not be a concern if the leading hero has a high defense skill.
• Another thing about the tower in castle combat is that is is never destroyed; it keeps shooting once a round as long as there is still some of the defending army remaining. BUT, if the single remaining stack is blinded, or paralyzed, then the tower doesn't shoot. Why? Because the immobile stack is not actually in the battle! So Paralyze or Blind the single remaining stack, and then you can gang up on it without worrying about the tower. If just your shooters attack, blind or paralyze the defending army again afterwards to continue the effect. This applies to fighting enemy heroes also; Blind or Paralyze the single stack, and the enemy hero won't be able to cast any spells, because their troops don't get a turn!
• This is about the potential of the Berzerker spell. When in battle, cast Berzerker on the fastest enemy troop. When it is that troop's turn, the hero can't dispel it because the berzerked stack acts automatically. The berzerked group will attack the nearest stack, whether friend or foe! This is a good spell to use when attacking a heavily defended castle, since being penned behind walls, the berzerked troops can just about wipe out the other troops! This is especially true when capturing the final castle in scenarios 5 through 8 in the campaign game, since the final castle will have at least 50 of each troop, so they can do a lot of damage to each other while you watch! Beware, for the computer will use this trick on you as well!
• If you ever wanted to control all 4 kingdoms from start on a multiplayer map, you can! Just start the program, click on NEW GAME, MULTIPLAYER, HOT SEAT, 4 PLAYERS, choose the map you would like to play, and then get to it! Now you know how to play those multiplayer scenarios by yourself!
• Do you want to play multiplayer games with just 1 player? Do the above steps, then right when you start, save the game, click on LOAD GAME, STANDARD GAME, and open the game you just saved. It will ask if you want the computer to control the other 3 players, just say YES. Now you can play as the only player in multiplayer games, starting with just one kingdom.