Rushing is very complicated and how you do it is based on how many players and which race your opponent is. When you rush, it is a good idea to be Humans, though you could be Undead or Orcs. Night Elves are not very good rushers unless they have other races supporting them. I will divide this into 3 sections, one for 1v1 rushing, one for 2v2 rushing, and one for 3v3 rushing. Please note that it is a bad idea to rush against Humans. Also, rushing is very ineffective against higher level players, and they will usually hold of your rush and counter. Rush at your own risk.
(It is strongly advised that you be humans for these strategies)
The key here is to get an army AND a hero very fast. However, if you know where your enemy is, you can do a:
Militia/Archmage rush: Note that this rush is highly risky and very easy to fend off by even mediocre players. Make all 5 peasants construct the altar in the beginning and get an Archmage. The Archmage should learn Blizzard. As soon as he is ready, make all your peasants into militia. On arriving at the enemy base, cast Blizzard over the gold-miners of the enemy and set your militia to work. Back at your base, you should be rebuilding peasants to replace the ones who went off to war, in case the rush fails. After eliminating enemy workers, destroy the barracks/altar (depending on which they have) and any units they may build. remember to make sure that no peasants are built. Back at the base, you should have a barracks. Send the Footmen you produce here to help finish off the enemy.
Archmage/Footmen/Militia(optional) rush: Use the same strategy as before, except, after you get the Archmage, do not attack immediately. Also note that you can get Blizzard OR Water Elemental as the first spell. Set some peasants on chopping wood, and as soon as you have enough (and a little extra) send all wood-choppers and builders to build a barracks. Produce 3 footmen and you're off. You can take militia with you, but it is not required. Continue to build peasants at your base and create more footmen. Make your barracks a force (Control-#) so that you can hit # (the one you chose for your force) and then "F" so that a Footman is immediately under production. Also, place the rally point for your barracks in the enemy base.
It is strongly advised that at least one member of your team (preferably all) be humans for these strategies and that none be Night Elves
The idea here is similar to before however, there is a twist. You can use either of the above strategies (but doubled, attacking the same base) or one of my personal favorites:
The Barracks rush: Create an army as in the Archmage/Footmen rush and send them just outside the enemy base. Note that your Archmage should have Water Elemental as a spell. Have your ally join you. Both of you build barracks (use 2-5 peasants) and begin producing footmen. When you feel ready (or when they find you) attack. Keep up a steady production of footmen as you destroy the enemy base.
It is strongly advised that at least one member of your team (preferably all) be humans for these strategies and that only one (max) be Night Elves
3v3 rushing is very similar to the other rushing techniques, though much more likely to fail. Because there are three enemies to deal with, it has to be very coordinated. All of the above strategies apply, and there is one more. It works in the other scenarios, but only really shines in 3v3:
Harassment: This is a simple strategy using either the Paladin or the Archmage for Humans, the Demon Hunter or Keeper of the Grove for Night Elves, the Dread Lord or the Death Knight for the Undead, and any hero for the Orcs. It works best for the Humans, as they can get altars a lot faster. You immediately build an altar and as soon as you are done, each player sends hero to a different base. Your objective is to disrupt, NOT to destroy buildings. The enemy will be very confused. The important part of this is to keep up your base production and to look out for your hero at the same time. Three Archmages with Blizzard or Water Elemental is very effective, and can wreak havoc. As their bases are completely disrupted, you can build up a nice army of footmen to crush them with. It is VERY important to keep your hero alive, so that your enemy is constantly afraid of attack. Use your Town Portal scroll to escape, if you must.
That sums up rushing in WarCraft 3. These are the methods I have used effectively, or seen used effectively. If they don't work, it's your risk to try them. Good luck!
In all rushing scenarios, the altar must be completed quickly
The crucial first battle. If you lose this, the rush is over
Water Elementals are a great asset and can be used when your footmen have died
Keep your barracks pumping Footmen: Reinforcements arrive to finish them off
I have only killed a few peasants, but they are forced to stop production to deal with me
During the last attack, I killed gold-mining peasants, now they only have three
A quick and seemingly successful attack encourages other players to leave the game