Im a little stuck here I am running a Vox AC4TVH into the matching 16 ohm cabinet.
I would like to buy another cabinet and run the two 16 ohms cabs using the single 16 ohm output.
Would I need to buy a cabinet splitter or something like Radial (I think?) sells?
Am I supposed to use 2x 8 ohm cabs connected to the single 16 ohm output and split them or something.

I may do this sometime in the future with my other amps so it would help if someone could just give me a basic idea on what to do.

Unfortunately if you only have 1 16 ohm out you will onliy beable to run 1 16ohm cab. 16ohm + 16ohm = 8 ohm. if you have a 8 ohm out you can daisy chain the cabs to make it 8 ohms though.
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^ I don't think there will too many situations where running 2 cabs (even in a 'daisy chain') will result in an additive scenario with the impedance ( like 8+8=16).

I believe that the AC4TV can only run 16 ohms. There for if you want to run 2 speaker cabs - my suggestion is to contact Vox and follow their recommendation.