You can a) register via email (one chance of winning), b) take part in Challenge one as defined in the terms and conditions, which is submitting your favorite / best Chaos Software project for another chance, and c) submit for challenge 2, sharing a birthday specific rendering for a third chance.
As far as I am aware, you could submit multiple images for each category, though this doesn't let you "win twice" (so if one image is picked as a winner for, say, the birthday render, any other birthday renders you also sent in would then be ignored). Don't go crazy and submit your whole portfolio though :) But if you have 3 or 4 images which you think are your best, and can't choose between them to pick just one to send in, afaik that is fine. You can always submit a ticket via
https://support.chaos.com/requests/new to ask, so that the question gets direct to the folks who oversee processing the entries, just to be sure!