The first step in Upgrading... is to Snow Leopard = OS X 10.6.x
It is Not available as a download... It is a Paid Upgrade.
Do this first...
Check that your Mac meets the System Requirements for Snow Leopard...
Snow Leopard Tech Specs
If so... Purchase a Snow Leopard Install Disc...
After the Successful Install, run Software Update to get the latest updates for Snow Leopard.
Be sure to make a Backup of your Current System Before Upgrading...
First find out if you are ready for 10.5: https://discussions.apple.com/docs/DOC-2275 (which you can skip if you are ready to go to the next step).
Next find out if you are ready for 10.6: https://discussions.apple.com/docs/DOC-2455 (which you can skip if you can get ahold of the hard to find USB Flash drive version of 10.7 and are ready to install on a hard drive without an operating system).
Then 10.7: https://discussions.apple.com/docs/DOC-2465
You have to have Snow Leopard as a start.
1) Make sure your computer meets Snow Leopard technical specifications - http://support.apple.com/kb/SP575 This mostly means making sure it is an Intel Mac and has at least 1GB RAM (at least 2 GB is recommended). Go to the Apple in the upper left corner of any window to "About This Mac". Does it mention "PowerPC" (not Intel), or Intel? To check RAM continue to "More Info...". It should say you have at least 1GB of "memory".
2) Buy a Snow Leopard disc from Apple online
or telephone Apple. In the USA: (800) 676-2775 (contact information for other countries: http://support.apple.com/kb/HE57)
Alternatively you can buy from online retailers but anticipate paying much more than the original price which is the price still charged by Apple
3) Backing up your computer before upgrading is always a good idea.
4) After installing from the DVD, update your Snow Leopard installation using Software Update or manually downloading and installing the Mac OS X 10.6.8 Update Combo v.1.1 - http://support.apple.com/kb/DL1399