A drill press would be nice, but if you file the pin flat first a hand held drill works. Take your time and go slowly. A good bit helps too.
I second the small indent in the anvil part of my bench vise. It helps keep the razor in place while you are pinning. I got my hammer at the local craft store, they had very small ballpeen hammers there for jewelry making. I would recommend starting with brass pins, they were much easier for me to get right than nickel.
Personally I don't like using a drill unless absolutely necessary. I prefer to remove the peened head and use a pin punch to knock the pin out. Using a drill can work if you have the alignment perfect but it's very easy to end up with an egg-shaped hole otherwise. Once that happens, when you go to re-use the scales your alignment will be a pain. If the scales are broken and going into the garbage it doesn't really matter. There's also the matter of damaging the drill's cutting edges if you hit the hard steel of the razor.