Hi Jeanette,
First thing you have to do is make the map with Krom's editor. Then save the map file in KaM\data\mission\mmaps\MapName.map. The name must not contain spaces!
Then you have to make the mission file. In my editor, click New and choose Multiplayer as the mission type. If you want it to be one where you build a base then use just "Multiplayer". If you want it to be a multiplayer battle only (no buildings) then use "Multiplayer - All Fighting". Select the map file that you made, and it should all load up ok. Add the buildings, troops, etc. for each team using the Placement tab on the left and set the mission options using the Treeview tab.
Then save the mission file as KaM\data\mission\mmission0.dat. (backup the previous version first)
Start KaM, and use the FIRST multiplayer map in the list. (doesn't matter what it is called, the first one in the list will always be the file mmission0.dat) Choose your teams and start the game! If you did everything correctly then it should work fine. Otherwise, post back here explaining what happened and I'll try to help you further.
If you get stuck you can try reading the help file for my editor. (click Help -> Help) It has some interesting information, it might help you when unexpected things happen. It doesn't have much about multiplayer though, it's kind of focused on single player as that is the main mode of the game.
Oh, and keep in mind that multiplayer in TPR can be a bit buggy. Units get out of synch and weird stuff. It is best to use TSK if possible, (these instructions are still correct) but if you can't then never mind, it will still work ok.
I hope this helps you,
Lewin.
P.S. Don't forget to copy both of the files to each of the computers! If you don't then you will all be playing different missions.
Just put them in the same folders with same file names and it should work fine.