I’m almost positive there are many links on this site on how to use Abattlemap - up to and including how to make your own games with it.
Nutshell:
1) You can move pieces individually, 5 at a time, 10 at a time or all at once by using combinations of shift, tab and shift-tab. Play with the map to figure them out.
2) The game will automatically track the value of your income, you just have to remember to put a “flag” down.
3) To get new pieces you click the icon you want in the “toolpieces” and click the map. The same shit, tab and shift-tab functions will work.
Then the only trick is figuring out what pieces are what. Secret: Put it on the board and look in the “info” box, it will show the IPC increase in units for that country on the board. That’s how I figured them out back in the day. They are also listed from lowest cost on the left to highest on the right - in order of unit type (land, air, water, facilities). Could be wrong on some modules, but that’s pretty much standard.
Start a game: File>New>Map