General methods for detecting torsion in a homology theory

Question

I am just wondering if there are any general techniques one can use to detect torsion in a given homology theory. I have vaguely heard that spectral sequences can be used to do this, but I do not understand how (nor do I really understand much about spectral sequences). I would like to be able to have some tools to show that a given homology theory has no torsion.