We recommend  for a comprehensive survey of integer relation algorithms. That paper also presents a unifying view of several types of algorithms that at the first glance seem to be different in nature. Since our paper is application oriented, we restrict our brief presentation to the two types of algorithms for which implementations are accessible to us (and which then are surveyed in Section 4).
Since an implementation of the LLL (Lenstra, Lenstra, Lovász) algorithm is available in almost any computer algebra system, we discuss the LLL-based methods in more detail (Section 2.1) because it is conceivable that the reader would like to play with the respective integer relation code. In the case of the PSLQ algorithm, whose implementations are much more efficient but less directly available, we restrict ourselves to stating its most important features (Section 2.2) and we refer the reader to appropriate sources for a more technical discussion.