It's really pretty self-explanatory.
What have you tried and what were your results?
I suspect that the principles would lend themselves to a step by step but how the effect works with your specific video will depend upon the degree of shakiness and other factors.
1. Your video clip on the Timeline of a project with the project settings which match the properties of your source video (part of all works whether or not the Stabilizer is involved.
2. Go to fx Effects Tab at the bottom of the Expert View, navigate to the Video Stabilizer and click on it to view its thumbnail. Drag the effect's thumbnail from there into the video clip on the Timeline.
3 I ran into an online excerpt of the Video Stabilizer in Adobe's Classroom in a Book, you may want to follow the path from there.
http://books.google.com/books?id=7zdjWNElM1IC&pg=PT252&lpg=PT252&dq=premiere+elements+stab ilizer&source=bl&ots=YM4HHrmZAl&sig=MpFt6GJn7IkgESWBZ6sC6wA7aEM&hl=en&sa=X&ei=ZZ2zUbbVI5W3 4APDq4D4DQ&sqi=2&ved=0CHoQ6AEwBw
Also, you might want to put that information together with Adobe Effects Reference's description of the options iin the Applied Effects Palette/Stabilizer Panel.
(Scroll down until you get to Video Stabilizer options description.)
The above should supply with good starter information. If you need clarification on anything that I have written, please do not hesitate to ask.