How do I upgrade from 10.5.8

Generally, you need a Mac OS X 10.6 DVD; these are available at the online Apple Store.

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You need to purchase Snow Leopard:

Mac OS X 10.6 Snow Leopard - Apple Store (U.S.)

If you wish to upgrade further, and your machine meets the minimum requirements, you can subsequently call Apple to purchase Lion, or upgrade directly to Mountain Lion from the App Store in Snow Leopard.