First of all, the rules of Asexual Jo follow all of the basic rules for Classic Jo, which you can find here.

In addition to those rules, you have the ability to split and combine. Every turn, you may either take your turn normally, or you can split. When you split, you make two moves instead of one, and you move in two directions off of your current position. Each of these moves becaome their own heads. Each turn now consists of moving each of your heads one space. You may split your heads infinitely, but if any one of your heads can't move, then you lose the game.

The only exception is combinding. If two of your heads hit eachother, than they become one head again, in the spot where they hit, thus combinding.

This might be hard to understand, so here is an example.

Player 1 begins by moving normally.
Player 2 then moves normally.
Player 1 then splits, and moves two seperate directions off of his previous move.
Player 2 then moves normally.
Player 1 then has to move each of his two heads one space.
Player 2 then splits.
Player 1 then moves one of his head one space, and splits the other head. He now has three heads.
Player 2 now moves normally, (moving both heads because he split).
Player 1 now moves normally (moving all three of his heads).
Player 2 now combines his two heads, because he moves them into eachother.

The game continues.