There are no steps that you need to take yourself prior to actually contributing. Just go ahead and start. Pick a bug, or a feature, that you'd like to have implemented, and do it. If you go for a larger feature, it's a good idea to ask emacs-devel first, though, since there might be objections to your intended design or interface, and you better collect feedback before writing a thousand lines of code :)
If you are done, or if you are at a point where you'd like some feedback about your changes, mail a patch to the bug report (if there is one), or to emacs-devel.
If it's your first contribution below the cumulative 15 line limit, and if there are no technical objections, you'll find your change merged quite fast. Emacs lacks man-power, and is glad for any contribution it gets. I got my first simple patch merged within a day.
If you are over the 15 line limit, you'll be asked for copyright assignments. There is nothing that you need to do in advance, though: You'll be guided through the process. Note that copyright assignments are mandatory: If you refuse to sign, you are barred from contributing to Emacs. Even if your patch is technically perfect, it won't be merged for legal and political reasons. Hence, I never contributed a second patch: I don't want to sign any assignment.
If you have signed one, and completed the process, you can however just continue to contribute as before, and at some point, if you make continuous contributions to Emacs, you'll eventually be given write access to the repository.