Here is a list the 10 most common EDH formats – including rules.

1-1 EDH
Traditional EDH with 40 life points

2HG (Two headed giant)
Turn i clockwise and you share both turns, live, attack and defence. Each opponent spells i good here. Surge spells and storm abilities also, thus you can collaborate with your team mate. You don’t get to see your team mates cards, but it’s more or less okay to indicate move and tactics in casual play, that reveals your cards. There is no commander damage.

This format is way quicker than any other format.

In casual play, you should not make to strong synergies beetween your team mates decks. And never have 2 of the same commanders – it becomes ridicolous good. Abilities like Heartless-hidetsugu, that can kill instantly. Sorin Markov and Magister Sphinx is also Overpowered in this format.

3-ways
Like traditional EDH magic, but tends to force very long and boring games. Very often the one that is third in the starting other, will have very bad odds for winning. If often ends up win conditions like kill or be killed round, where one player decides who will wind, but cannot barge because the game will end within 1-3 rounds.

4-ways
Like 3-ways but it becomes more tactical and random who wins. Barging with opponent, make allies and help others will be a natural part of the game and turn this into an all-nighter or if you are lucky just 2 hours.

Pentagram

The winning player is the one, that first kills the two opponents that i placed directly across of him. Funny and engaging, but it takes long time, before its your turn again. Lots of politics, but unfortunately this games often end up with several winners.

General (3 vs. 3)

My favorite style and gameplay. Each group of three has individuals turns. They are placed on each side of the table. In the middle is the General, that has 40 lifes and on the axis the helpers that only has 20 lifes. You cannot affect more that 2 players away – which means that a board wipe will all but one opponent – which is the one across the table. If you are first turn order in your team you can play spell like howling mine, mana flare and other global help spell, thus your team mates will have benefit of this before your ooponents. If you are last turn order, you don’t wanna cast global help spells.

Tiny leaders

Only 50 cards and 25 life. Your commander cannot have more CMC that 3. There is no commander damage in this format. There is an individual banlist for this format.

Oathbreaker

The newest of them all. Besides a Planeswalker as commanders, you also have a signature spell, that is an instant or sorcery.

60 cards, 20 lifes and no commander damage.