Well, I have a Dremmel tool with a normal drill bit. In case you're not familiar with a dremmel tool, it's a hand held rotary tool, similar to a drill, but it turns at a greater RPM, and can be used for grinding, sanding, drilling, cutting, polishing etc. I use the dremmel for many items that surround a circuit, such as: Grinding holes in cases, cutting excess metal away, trimming PCB etc. I use a 1/16" drill bit for most of the holes for the pads. You can go smaller, for the smaller gauge lead wires, or larger for the larger gauge lead wires. Generally, 1/16" does the job for most applications.
Of course, you don't need to use a dremmel tool. You can use a power drill, hand drill (crank style drill, or push pull drill). I've even got away with drilling holes using a twisting motion with a drill bit and my fingers, but drilling many holes this way is a waste of time.
One point to consider, make sure that your drill bit wont drill out the entire pad that you've made, otherwise, soldering the component to the trace will be quite a pain in the neck.
Another point to consider, always drill from the copper side through to the uncopper side. If you do it the other way around, you'll have a rough hole where your solder joint will be. Sometimes the phenolic or epoxy glass burrs will get in the way, and provide for a crappy solder joint. Also, if you drill the other way around (through the uncopper to the copper) you may lift the copper from the board and potentially crack a trace, or your pad.
Also, drill nice and easy. Let the drill bit do the work. Applying excess pressure will set you up to slam the board when you break through, thus potentially cracking the board, or make a crappy hole.
Also, you'll probably want to clean the board, once you're done drilling, just to get all of the fragments and finger prints off of the board before you solder. Those fragments can really screw up a solder joint.
Also, if you're having trouble keeping the drill bit centered on the area that you want to drill, try using a small screw driver to indent your center point before drilling. Just hand pressure will normally do the job. Don't pound on the screw driver, or you might crack the board. The small indentation (Center punch) will keep your drill bit in that zone, while you start to drill.
Finally, try to design so that your holes will be away from the edge of the board. Sometimes, you can crack the board by drilling near the edge, or provide for a weak point in your structure. This isn't a big issue, but a point to consider when designing your layout. A good 1/4 inch from the edge is pretty good. Of course, you can get away with drilling near the edge, but sooner or later, you're bound to crack a board.
I'll post a link to a site that gives a tutorial on this subject. I have to find it first.