Yinsh is probably the easiest of the GIPF games to learn. The goal of the game is to capture three rings of your own color. You first place five rings on the board, then each move pick a ring to move. Moving a ring leaves a chip behind, and changes the color of all the chips it passes over. Whenever a row of 5 chips is created, they are removed from play, along with a ring of the same color. There are a few subtleties in the rules, but that's the basic idea.
This looks vaguely similar to Othello, but it is much subtler because removing the chips creates new open space, and removing a ring (progress toward winning) weakens you.