I got OS X 10.3.9 install but want to upgrade it to 10.7. How do I go about doing it?
It is impossible to upgrade from 10.3.9 to 10.7 or 10.8. This is because Apple stopped using the PowerPC processor architecture after 10.5. The farthest you can upgrade to is 10.5. You can purchase a installer disk on the apple website. However why don't you consider getting a new Mac? 10.5 is very outdated. Or as Orgon says, try Linux. It does not require much processing power and you have many different distros to choose from. Check out these MakeUseOf Guides if you want Linux
As Jan says, you can only update to 10.5 "Leopard" and unfortunately, the earliest version you can buy directly from Apple is 10.6 "Snow Leopard". You can get Leopard discs on eBay, but they tend to be quite expensive, usually around $80.
If you don't want to spend that much, but are keen to update your Mac, you may want to consider installing Linux on it. There are several current versions of Linux which will run on a Mac with a PPC processor, but check the compatibility list carefully to make sure your specific Mac is supported.
I'm afraid you will not be able to update that far!
10.3.9 was a PowerPC only OS X version wherein 10.6 and later are Intel only versions.
The latest one you will be able to update to is OS X Leopard 10.5. This version is no longer sold but you may have some luck finding it as rest-stock in some online shops or on eBay.