Choose About this Mac from the Apple menu and check the processor.
If it's a G3, no further upgrades are available.
If it's a G4 or G5, buy a retail Mac OS X 10.5 DVD from a source such as Amazon or eBay; Apple still might have copies in stock if you phone them.
If it's an Intel Mac, buy a Mac OS X 10.6 DVD from the online Apple Store.
Note the 867 Mhz or higher (1 Ghz is higher) is necessary for 10.5.
Note 10.5 also gets rid of Classic, the compatibility for Mac OS 9.
Note 10.6 to 10.6.8 can be upgraded to 10.7 or 10.8 as long as you have a Core2Duo minimum. 10.7 or later are not compatible with Rosetta, the Mac OS X tool that lets pre-2006 software run on newer machines. For more on each, see these tips on 10.4, 10.5, 10.6, 10.7, and 10.8.
If you meet the requirements after purchasing the 10.6 installer CD.
10.4.4 through 10.5.8 can be upgraded directly to 10.6.3 to 10.6.6 to 10.7 to 10.7.5
10.4.4 through 10.5.8 can be upgraded directly to 10.6.3 to 10.6.8 to 10.8 to 10.8.4
10.7 & 10.8 are separate purchases, and can be downloaded from the Mac App Store once you are at 10.6.6 or 10.6.8 minimum depending on where you are at.