Use a external hard drive.
There is multiple ways you can backup. Each one is different.
1. You backup things that cant be replaced, pics, music, personal things like that. Then you put in a new drive and do a fresh reinstall. You have to reinstall everything.
2. You get a new drive, hook it into the system as a 2nd drive and image everything from the bad drive to the new. If all goes well everything will be there. No reinstall.
3. Use a backup image software that will image your whole drive and store it on the external. Then put in a new drive and restore the image. Everything will be there. no reinstall.
The problem with #2 & #3 is the bad sectors. What ever data is on those sectors isnt readable. So you can try the image and hope for the best. No matter what backup your important stuff just in case
Shane