The first thing you'll want to do is make sure you have a full backup of your stuff on an external drive.
Next, If your drive is quite full delete some of the stuff you don't really need. You'll likely need to trim down as SSD's tend to be smaller (cheaper) than HD's. You'll want to leave 1/3 of the SSD free for a 256 GB unit and 1/4 for a 512 GB or larger. So trim away!
OK, the next step. You'll want to get a SSD that can work in a SATA II (3.0 Gb/s) system. Take the time to review the spec sheet if it doesn't state it supports SATA II you'll need to find another SSD.
You also may want to up the RAM if you have a 4 GB model. I would go to 8 GB (light user) or 12 GB.
Now go to the App store and download the OS installer if you don't have it in your Apps folder already. I would recommend making a copy then create a bootable USB thumb drive. First reformat the thumb drive using Disk Utility with GUID partition mapping and format the partition Mac OS Extended (Journaled) the launching the copy of the installer to install the OS onto the thumb drive. This serves two functions one to get you comfortable on what you'll do with your SSD when you install it and create a boot drive just in case!
Follow this IFIXIT guide to take your old drive out and put in the new SSD in, as well as replace the drives SATA cable as well as thins series has a known issue with them: MacBook Pro 13" Unibody Mid 2010 Hard Drive Cable Replacement. Here's the better cable: MacBook Pro 13" Unibody (Mid 2012) Hard Drive Cable - Apple P/N 923-0104.
Once the new SATA cable & drive are installed you'll need to boot up under either your old drive or the thumb drive we created to install a fresh copy of OS.
You'll still want to hook up your old drive to your system so you can leverage the Migration assistant to bring everything over. You'll want a SATA to USB adapter cable like this one: Startech 2.5" SATA to USB adapter.
Don't worry, If you have any problems were here to help!