The tick is full - that's why it's going black. (it's full of blood)
You may want to use a tick hook, especially for the first time, but I have used eyebrow tweezers - on dogs, lambs and humans. It will take less than a minute.
The temptation is to squeeze the tick with the tweezers, which you mustn't do, as it will break up, or as someone else has said, you could leave parts of the tick body - now partially buried in your cat, inside.
Hold the tweezers firmly, get someone to hold the cat still, and grab the tick - pull slowly with a clock wise or anti motion, not just upwards. Ticks burrow.
Ticks live in vegetation, and drop off when they find a new home. They can't leap or fly.
Here's some more info.
http://www.bada-uk.org/