Alpha-Beta pruning is not a new algorithm, rather an optimization technique for the minimax algorithm. It decreases the computation time by a huge factor. This allows us to explore much faster and even go into deeper levels in the game tree. It cuts off branches in the game tree which need not be explored because there already exists a better move available. It is known as Alpha-Beta pruning because it passes 2 extra parameters in the minimax function, namely alpha and beta.
You just have to compare the results of the alpha-beta algorithm to the simpler MiniMax one. As soon as they disagree you've got a bug in one of the two algorithms.
That simplifies the problem to testing whether your MiniMax algorithm is correct and well I can't think of any special tricks for that - but since it's a recursive function it should be possible to write unit tests for all cases.