Yeah! Its fairly simple.
1) Remove your old HDD from the system
2) Install your new SSD
3) Install OS on to the new SSD
4) Go into BIOS and ensure that the SSD is set to the top priority in the Boot Order
5) Reinstall your old HDD
Most things will work just fine after this (games, music, documents etc), however some programs will not like the fact theyre no longer on the 'C' drive, and will have to be reinstalled - but the bulk of the work is as easy as that.
At this point, youve technically achieved your goal. However, you're obviously still left with your old OS files on your HDD. Either delete the folders manually or...
6) Transfer any files you want to keep over to your new SSD
7) Use Disk Manager to format your HDD
8) Transfer files back from your SSD to the HDD.
Doing this will require some extra work to get your games to work, as a lot of game files are kept in the 'App Data' and 'Documents' folders.
Do you have most of your games on Steam?