I'd advice against moving your whole game library onto an SSD, if your HDD is 7200 RPM then games will load just fine. If you want to move a couple of your favorite games then it varies, but always find the save files from your games and back them up to another drive.
Steam Games- If you want you whole library moved then sign out of steam, go to the steam installation folder usually C:\Program Files (x86)\steam, delete everything but steam.exe and steamapps (this is where your games are), copy/cut those two files on your ssd in where you want future steam games to be installed to, then click on steam.exe and it will update/download other files while keeping your game files.
GOG and other DRM-free games, these usually you can copy the...