Combat
While unit match ups and having more units than the enemy can allow you to win battles, casting spells and unit control also has a major impact on battles. It's possible to have more units, more upgrades and still lose battles because the enemy has better unit control and is better at casting spells. Focus on using spells, properly leading units into combat, and picking good targets to attack.

Group Control/Healing During Battle
During a battle, group select your units that are engaged in combat. Look at the information window and watch the unit's health. When you see a unit is about to die, double-click on that unit's portrait. That will select him out of the group. Now, command him to run away. This can allow him to survive, and hopefully, get healing and return to fight another day.

You can also use this method to heal units during battle. When you are using the Paladin, you can select Holy Light and left-click on the portrait of a damaged unit to have the Paladin cast Holy Light healing on that unit. This method is much easier than finding the unit in a battle among troops. You can also use this method with Human Priests or a Troll Shadow Priest to heal a unit in a group.

This method can also be used with other spells and abilities such as the Druid of the Claw's Rejuvenation.

Don't Be Afraid to Lose Units
While it's good to save any units you can for a later battle, do not become so protective of them that you are afraid to use them.

Run Away!
If you see yourself in a battle that you just can't win, run away. This can give you time to reach reinforcements or at least annoy the enemy commander. If possible run back to towers or an ally's army.

Seek out and destroy enemy expansions
The enemy may/will be seeking out additional resources. You should be scouting the Gold Mines on the map to make sure the enemy is not building at them. If you find an enemy expansion that is not defended, immediately attack. Sometimes the enemy defends their expansion very well and has no defenses for their main town. If this is the case, attack their main town instead.

If You Win a Battle, Attack Their Town
If you significantly win a battle, immediately attack the enemy town or expansion. Often they do not have a back up force or defenses to protect themselves now that you have taken out their main force. When you win a battle, push your advantage further rather than sitting back and building up.

Combat Takes Precedence Over Everything
Battles in Warcraft III require a lot of micro management. You often cannot just tell your units to attack and move on to other things. You must control your units throughout the entire fight. Do not move the screen back to your town and start working on building. Watch the battle! Make sure there won't be any opposition before taking your eyes off of the battle. The only reason you should leave a battle is to quickly train more units or instruct recently completed units to the battle. In these cases, pick a good time to move from the battle and quickly return to the battle once you've finished giving new commands.

Misses
Splash damage units that get a "Miss!" from Curse, Evasion, Drunken Brawling, or Drunken Haze deal 1/2 damage to targets.

Mixed Forces
Generally, it is best to have mixed forces capable of attacking both air and ground units. That way if enemy air units attack you can respond. It is also a good idea to bring siege units if you plan on assaulting a town so you can finish it off quicker.

High Ground
Ranged units (Missile) will miss a lot (25% chance to miss) when trying to shoot up to higher ground. Whenever you see the red "Miss" notification, instruct your units to charge up the hill to the same level as the enemy. On some maps such as The Crucible or Lost Temple, enemy players might build towers at the top of their ramps. You should use Siege Weapons and something to "spot" for the Siege Weapons and clear out the towers before heading up the ramp. Don't be placed in a situation where you're fighting from lower ground.

[ Click to Enlarge - 124 KB ] Push up to higher ground so you don't miss.

Alt Key
You should use the Alt key during battles to show which enemy units are nearly dead. You can then focus your attention on them and finish them off. It's better to be attacking a nearly dead unit rather than one that is at full health.

Beating Ranged Units
The best solutions are usually Siege Weapons, Area of Effect spells, or at least melee units rushing the ranged units.

Standing Around
Try not to stand around. You should either be attacking the enemy or killing Creeps. You can get scared and want to stand around and defend your base, but that's what the enemy wants you to do. They want you standing around doing nothing while they are out there gaining experience, expansions, or items.

Techers
Someone who "techs" attempts to quickly advance up the tech-tree to high-end units such as Knights or Sorceresses or Chimaera. This can be very damaging if you have lower tier units facing more powerful units. You need to scout the enemy and make sure they are not upgrading too fast. You can tell they are upgrading if their Town Hall is upgrading or they are building other buildings necessary for high end buildings. At this point you need to rush them to stop it. Techers are typically weak to early rushes. They often try to "harass" you with their Heroes to distract you from attacking their town until they are upgraded. They are not using their money for tier 1 (Grunts, Footmen, etc) troops.

Delaying Tactics
When people have a small army, have recently lost their army, are losing, or are quickly trying to upgrade to more powerful units, they may try to delay you from attacking. Typically they do this with hit-and-run tactics, either with a Hero or an entire army. What they will do is attack, then run, attack, then run, again and again. This can become very annoying, of course. Rather than falling for this you either need to attack their town or use Hero and Unit killing abilities to make them pay when they run. Don't fall for their tricks. Players also try this hoping to disorient you so you'll crack under the pressure.