Depends. Algorithms typically do one of two things:

1. impose system changes

2. produce or modify a data structure

The first is more challenging. The best bet is a good test environment. The second is simple: just output the data. I prefer to send it to html and display it as a table or tree formatted by css.

Care to elaborate on this? You mean as: you implemented an algorithm say in Python and want to visually see what happens (the flow)?