There are four kinds of things on the board, open spaces, red blobs, blue blobs, and blocks (the green squares). You can either spawn one of your red blobs into an adjacent open space or jump into an open space one square away. To visually get an idea of these rules simply grab one of your blobs (in this case a red blob) by holding down the mouse button on top of it and then drag it around the board. You should notice that when you pass over a legal move the blob is bright red but when the move is illegal the blob is dark red. Also notice that if the potential move involves jumping your source blob will disappear.
To make a move just let go of the mouse button. Now any enemy blobs adjacent to your new blob will become your blobs! To win you just have to end up (the game is over when there are no more free spaces) with the most blobs. Blocks simply are, they never go anywhere or do anything.