To completely upgrade a tank you need Tank EXP points. (Silver star you obtain after winning battles)
To go to the unlock tree you must choose which tank you want from your garage, press X to upgrade and then go into packages, It will then take you into a lovely tree.
The easiest tank to fully upgrade is the LTraktor, you'll need roughly 600 Tank EXP to unlock all packages on it. Which is around 3 games or so if you perform well.
You must unlock all packages of the tree including the tanks towards the end.
Another note is that you don't need to actually buy the packages, so you can save your silver. :)