Read as much as you can about assembly. Debuggers are your best friend. Pick a target (app, iPhone, xbox, whatever). Attach debugger and step through the code and learn possible entry vectors (buffer overflow, loading for arbitrary file i.e. pdfs, so forth). Once you have an entry vector you essentially have an exploit, the rest is developing that exploit to do something "useful".

Sorry for the shortness of this response, if people are interested I can throw together a couple of blog posts.