Yes you can replace a SATA-based 2.5" laptop hard drive with a SATA-based SSD. You can find no end of Youtube movies and webpages on the subject. The only complicated thing is to have the right screwdrivers to open the cover, remove any bar that holds in the drive and the 4 mounting screws in the sides of the drive.
For the 2010 MacBooks I work on, you need a small phillips screwdriver for the back cover and the hold down bar. To remove the 4 mounting screws, you need a torx screwdriver.
You can find pictures and procedures on websites such as www.ifixit.com.