+1

AngelList is awesome.

network for intros, preferably warm. failing that, just email the CEO directly. write a kickass email pitching yourself and detailing your skills. tactfully follow-up.

network some more.

founders have (and want to see) passion and hustle. show them you have these qualities and you shouldn't have trouble landing a paid internship if not an entry-level role.

last resort: get a few unpaid internships at startups you love. if one doesn't turn into a full time offer, you'll have some awesome experience you can use to get the attention of other startups.