Welcome to Cow Solitaire.
The aim of the game is to end up with one cow left in the middle of the field.
Click on the cow you want to move. The selected cow will face the right. Choose an empty space into which you want the cow to jump. When it jumps, the chosen cow must jump over one other cow and must move either vertically or horizontally. Cows cannot move diagonally as they find it confusing. To deselect a cow, click on it again to make it face the left like all its friends. To start again at any point, click on New Game.
There are a number of solutions pages. Michel Casabianca's Ohm Sweet Ohm has a graphical solution. Richard Seltzer's is a less elegant text version. To do it properly, however, you have to see Alexander Bogomolny's site, which includes mathematical explanations of the theory behind winning, as well as bibliographical references, variations on the game, quotes from Leibnitz, but no cows.
If you enjoyed this game, you might also enjoy the more interactive delights of my Cowthello, a JavaScript version of the board game Othello using cows instead of counters with simple computer opponent. Alternatively, I maintain a comprehensive list of Cow Games on the web.