Here's a real tutorial on how to play MUGEN online.

What do you need:
1.)2 players who trust each other and won't mess up their opponent's PC after a bad loss (I'll explain later).
2.)A little tool called LogMeIn.
3.)Fast internet connection and good hardware on each PC.
4.)A MUGEN that is working

The process:
Here's some description on the roles. Player 1# is the one who will connect to Player 2#'s PC. Player 2# is the guy whose PC will be used, so he's the one who should have MUGEN set up :P.

Player 1#:
So, go to this site, and register an account. Install the program on your PC, then go into your account. At the "My computer" window click on "Add computer". From the upcoming options, choose "Deploy LogMeIn IT Reach to remote computer(s)", and then click continue. At description, you can enter anything you want. Expiration date depends on you. Click continue again. Copy the link and give it to Player 2#.

Player 2#:
Use the link Player 1# gave you. Enter a name for your PC (can be anything), tick the "I have received this link from a trusted source" box, then proceed. Install the software, then tell Player 1# the access code you specified for you PC using LogMeIn. Also set you screen resolution to something small, decreases lag.

Player 1#:
Go to the "My Computers" window. Click on the PC of Player 2#, wait for the installation of the FireFox plugin (only tested on FF), and after it's done use the access code what Player 2# gave you. Now you are in the user interface of LogMeIn. Use the "Remote Control" function, and tada!: You can see what Player 2# can see on his monitor. You can control his PC just like you are sitting in the front of it. You can use your keyboard and your mouse as you'd normally use at your own PC (express some stuff like ctrl+alt+del, but the interface has special buttons for that.). Set the picture quality to "performance" so it won't lag that much. Now run MUGEN and you are ready to play!

WARNING!
Player 1# can fucking fry Player 2#'s PC if he's such an asshole. So Player 1# must be a trustable person who you know won't mess you up.
Other thing: Player 1# mustn't restart Player 2#'s PC via the user interface of LogMeIn. Fucks up drivers for some random reason (so after windows logs in Player 2# won't see anything.). Can be fixed in "Decreased Mode".
Also, I'm not responsible for any damage you cause to your PCs, it's your own dumb fault if you mess things up.

I hope you've found this useful, happy playing!