What is the best way to go about living aboard for about 5 months after college graduation?

Answer 1

http://travel.state.gov/passport/passport_1738.html
If, you can make a trustworthy friend over the Inet this can help too. I know many friends of mine do this and in return can help those people with inexpensive places to live when they visit here.
Also, browse the Web on the area you want to live. Find sites for renting an apartment and those things.
Another option may be Volunteer work. Maybe an Archaeological Dig. A lot of this going on around the world.
Here an Example, scroll down to Volunteers;
http://www.israel-mfa.gov.il/MFA/History/Early%20History%20-%20Archaeology/Israel-s%20Archaeological%20Treasures%20-%20The%20Mediterran
Somewhere I browsed the other day had all kinds of Archeology Volunteer stuff. It could be fun and exciting. Plus they may help with inexpensive places to stay and where to eat, away from the tourist traps. Most have plenty of Leisure time for some fun, heck, it volunteer work.