I would narrow it down to four GENERAL ways, although there are different methods within each path.
1. U.S. Coast Guard Academy - pretty obvious... four year college, commission upon graduation. About 40% of the officer corps in the Coast Guard came from CGA.
2. Officer Candidate School - historically OCs come through the fleet or from colleges (as gradutes). There is an active duty and reserve program.
3. Direct Commission - This usually involves certain specialties, such as lawyers or medical professionals from the private sector, or officers from other services. Direct Commission Aviators fall into this category (according to me....). You may get some cross-commissioning here too...
4. Other - I'm not entirely sure what it's called, but from time to time you'll see senior enlisted, or chief warrant officers, apply for officer promotions. I worked with a guy who was a public affairs chief, was selected for chief warrant officer, and eventually went "Warrant to Lieutenant".