By plane
capeair.com
By ship
Hyannis is the main terminal point for ferrys to Nantucket and Martha's Vineyard.
By bus
Cape Cod Regional Transit Authority
+1 800-352-7155, (http://www.capecodtransit.org/).Believe it or not Cape Cod actually has a pretty decent public transportation system in the summer time. There are buses from Plymouth and Brockton that run from Boston to Proviencetown and make stops at . The fare is about 15 dollars each way from Boston to Hyannis, which is pretty reasonable. The busses run every hour or so.
Once on the cape there is another option. The Cape Cod Regional Transit Authority as few viable options. The H20 bus--goes from Hyannis to Orleans and traveling down Route 28. It takes about an hour and half from start to stop, but this is also doable. In Harwich you can catch the FLEX bus that takes you to Proviencetown.
The Sealine Bus route goes west bound from Hyannis, along Route 28, until you get to Woods Hole. Where besides a few attractions is another point to catch a ferry to Woods Hole.
The Barnstable Villeger is a shuttle that goes around Hyannis. It is mainly used by locals. There is also something called the b-Bus which is for residents only Year Round or Seasonal but is basically a bus that will pick you up at your house or apartment--it is too complicated to explain here but you can visit the Cape Cod Regional Transit webiste.
The fare for all these buses is about 1-2 dollars each way.