Yes, this upgrade is relatively easy and a great way to add more space. You would need a 2.5" SATA drive which are relatively easy to find. I have been doing 1 TB upgrades with this hard drive found here:
I find that Western Digitals have high reliability and have very little issues.
When you get the drive I would download an application called Carbon Copy Cloner (Google it) and clone your old hard drive onto the new one which would require a hard drive connector. However, this isn't needed if you have a time machine backup in which case you can restore from backup.
The guide that you will need to follow to install the Hard Drive is here:
MacBook Pro 15" Unibody Mid 2010 Hard Drive Replacement
If you need any more info just leave a comment with your questions.
Hope this Helps