Click on the apple on the left of your menu bar at the top of your screen. Click 'about this mac' and it will tell you what level of OS X you have.
If you have 10.5, you'll need to call your in country online Apple store to order 10.5. In the US call 800-MY-APPLE. If you have less than 2GB of memory, you may want to consider upgrading for better performance. You can wait and see if 10.6 will work OK for you in it's 1GB minimum.
If you have 10.6 and want to upgrade to 10.7, again call the online Apple store. Make sure your system will support 10.7 before buying the upgrade.