this program is decent and simple to use:
just make sure you hardware includes nvidia graphics card (it uses cuda to speed it up greatly) there is a demo of the normal version, give it a go.
it really does wonders for shaky phone videos.
vReveal http://www.vreveal.com/ is made for stabilizing footage, and has a free version. Free version limits your output to a certain dimension however. I've used the paid version successfully one some stuff I shot with a spycam to smooth it out.