If you have 1GB of memory, you can upgrade to OS X 10.6 and OS X 10.7 with 2GB of memory, although 4GB is recommended.
To upgrade, call the online Apple store, which in the US is at 800-MY-APPLE, or order OS X 10.6 online at http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard . Install it, do Software Updates until no more are available, which will get you to OS X 10.6.8.
Once at 10.6.8, you'll need to call the online Apple store to buy the OS X 10.7 upgrade. They'll email you a code to use in the App store. Note with OS X 10.7 Lion that any PowerPC code will no longer run. So, for example, if you have Office 2004 today, you'll have to buy a newer version.