I have tried to find threads about my specific questions and googled it but was not successful so far.
I have bought a Phantom 2 Vision + without the camera and gimbal. The plan is to attach a cheap 3rd party gimbal (like the ones you find on Amazon) and use my GoPro camera.
I know, I will not have telemetry or FPV but this is understood. However non of the information I found do specifically tell me how to power up the gimbal. Although several of the gimbals claim they come with a cable to the power supply I have not yet found instructions, that show how to connect it. Is it as simple as plugging in the cable somewhere (i.e. the now exposed connections from he missing vision camera/gimbal) or do I need to open up the Phantom to connect or do I even have to solder things together? The latter would be very bad as I have not really good experience with soldering. And where exactly do I find the connector I need to connect/solder the power cable to? Hope somebody can give me the instructions for this.

You need to open up the Phantom.
Most aftermarket gimbals are 12-15V. Once open, on the mainboard you can see pos and neg. You can tap directly to this for 12V power.