The front pin is a spring loaded pin that you push in to release the front.
The rear pin is a "roll" pin and it must be pushed all the way through with a punch. Its best NOT to use a tapered punch. A straight punch, use a brass one if you have it, sized at 3/32 will work well, its just smaller than the hole, which is 1/8th. Line up the punch and hit it with a hammer. Don't whack it hard, a bunch of lighter smacks will work better than a couple hard hits because it allows you to punch through without marring your frame's finish.
It is easiest to punch out the rear pin first, then deal with the front pin, which takes only light pressure to push in and release.
If you really want the right tool, look for a set of roll pin punches. They have a little nipple on the end that fits in the roll pin, keeps the punch in place, and keeps the pin from getting peened over. I'll never go back to regular pin punches for roll pins.