If you just have one (or a few) to remove and don't want to buy a tool, you can simple pry up the inner center grey part with a small screw driver which "unlocks" the fastener. Then you can pry up the entire fastener around the outer edge of the black part.
Installation is reverse, with the grey part extended, insert the pushpin fastener into the hole then depress the grey locking pin down once it's in position.