This is a request that I have accepted to do.
First you need to have content manager downloaded on to your computer. Unless you are using the PlayStation 3 or Online Storage.
The easiest way to download is to plug-in the vita to the computer and let it automatically download or download content manager here
Go to content manager aka CMA on your PlayStation Vita.
Once you start CMA, you will be given a option to backup data on the Ps3, PC, or Online Storage. This tutorial is for PC so go to it.
Wireless would require you to register your device to the PlayStation Vita first. If you have CMA downloaded to your computer, your computer will automaticially connect to your vita once the registered device is selected.
Once you have selected your method of connection and the device to connect to (choosing device is only for wireless connection method) you vita will be prompt with this menu. Tap on "Ps Vita -> PC"
The next menu will appear and gives you the options of content you want to transfer. Since we want to back-up our saved games, go to Applications.
Now go to Ps Vita.
And wala. Choose what game you need to back-up and transfer it to your pc! Just select and copy to pc.
So when I buy my 32GB card, all I have to do is back up data on my 4GB and then I can transfer it to my 32GB?
Yes, once you do that, just copy all the content back to your new 32GB from a computer or ps3 or online storage.
If you have images, photos, or just apps you rather not re-download again. You can scroll down to "Saved Data" and back-up all content to the computer.
I do post often, I'm creating a website dedicating to Vita service.
Its still in the works but i just finished making my own theme creator for people to download and use!