Step 1- After you and your opponent meet over messenger (MSN, Yahoo, Google, etc) decide the format, usually Advanced Format, and if it is going to be a duel or match.
Step 2- Decide who chooses who plays first with a random method such as flipping a coin or rolling a die, your opponent calling heads or tails and you flipping for example.
Step 3- Duel! Communicate your moves so that you both know what is happening. This involves playing your cards as you would normally in-front of your computer then saying what you've done. Also communicate on which phase you are doing it in and confirm you are passing after your opponent's move.
EXAMPLE
Yugi: Hey Kaiba, ready to lose to me again for the 1 billionth time?
Seto: Shut up and duel me! A single duel, Advanced Format.
Yugi: Hey remember the top of school where I defeated you for the first time..? Heads or tails?
Seto: Tails... I don't recall...
Yugi: What about Death-T when I beat you for the second time after you failed to kill me and my friends? It's heads so I'll start. Draw]
Seto: Draws 5] No and neither do most of the people out there!
Yugi: How about Pegasus' Island where you threatened to kill yourself? SP]
Seto: Okay and I won that time!
Yugi: By cheating! MP1] I summon the Celtic Guardian!
Seto: It wasn't against the rules, it's a part of the time like timing out in a round. Okay.
Yugi: Cheater! I set 2 S/T.
Seto: Screw the rules I'm not actually here! Fine.
Yugi: End turn]
Seto: Draw]
Yugi: Remember Duelist Kingdom where I...
Seto: YES, I remember! MP1] I summon Lord of D.
Yugi: Ah the good old days, beating you every other issue. Okay.
Seto: I activate The Flute of Summoning Dragon.
Yugi: Fine
Seto: I Special Summon 2 Blue-Eyes White Dragons from my hand!
Yugi: Did you just summon a bunch of monsters in one turn? I activate Bottomless Trap Hole!
Seto: Noooooooooooooooo!!! Okay
Yugi: Done
Seto: Both my Blue-Eyes White Dragons are destroyed and removed from play. I set a S/T.
Yugi: Fine.
Seto: End turn]
Yugi: Draw]
...
...You get the idea.

If you have any questions post them below.