Magento upgrade is quite a tricky thing, so get ready to seat in from of your computer for several hours.
Actually you have two ways how you can upgrade your Magento:
The first one (as for me the easiest) is to use migration service Cart2Cart.
Install a fresh version of Magento and move all the data from your current version to a new one.
After data transfer you’ ll need to customize your store: template, modules etc.
This method is good, because you just have to go through the simple migration wizard and relax. The service will do everything else for you.
The second way is to follow a step-by-step Magento instruction, which you can find here.
This way is free. So your will be able to save your money.
Realize your skills and make a choice. It’s totally up to you!