Pseudocode for a searching tree
Probably the best way to explain how such an algorithm works is via diagrams showing it step by step for some examples, examples selected to exercise your code more or less fully (need not cover all left/right symmetric cases, for example).

If you use LaTeX, look for a package to typeset algorithms, like algorithm2e, and check out TikZ and it's facilities to draw trees. It's documentation is quite forbidding, search for tutorials or targeted explanations.

Place yourself in the shoes of your gentle reader: What would you like to see? What points of the algorithm are thorny? Any corner cases that need explaining? Any strange/surprising/seemingly useless lines?