You can apply the stabilizer effect by dragging it on the timeline.
Then render the timeline and play the video and check whether that helps you out.
Sent from my iPhone
He did answer your question, Coral.
Premiere Elements does include a Stabilize effect that can take the shake out of your video.
What version of Premiere Elements are you using and on what computer operating system is it running?
Although principles may stay the same from version to version, features are likely to be moved, changed, or discontinued. In the case of the Premiere Elements Stabilizer it seems to have survived the versions in one location or another.
For now I will assume that you have Premiere Elements 11 or 12 on Windows 7, 8, 8.1 64 bit. In that case, you can apply the Stabilizer Effect to your video via fxEffects/Video Stabilizer/Stabilizer. The Adobe Effects Reference document gives you some detail on the controls offered for this feature.
A few years back Richard Harrington did an excellent video tutorial on the Premiere Elements Stabilizer. I can no longer find it. But, the controls for the Premiere Elements feature are basic and exploration and experimentation typically tell the tale if it is going to work for your video or not. The feature details in the Adobe document cited, although limited, can assist you in this.
You will find scattered helpful tips on the Stabilizer in this forum, one example
Some opt for the more expensive non Adobe stablizer with more controls, and having presets. A reference to that has already been given.