Note:
    Procedure described here doesn't by any means give you a professional looking PCB, you can't use it for making PCBs for demanding circuits (very high frequencies, low voltage analog processing etc.), and the number and complexity of the PCB that can be done is somewheat limited by your nerve-breakdown threshold. ;)
    Still, it is decent procedure for making a smaller (number of) boards, plus it has its advantages at doing double-sided PCBs. I've even done some PCBs for SMD parts using this procedure.
 

Requierements:
    - copper clad board
    - prepunched prototype board with 2.54mm (0.1") grid
    - drilling machine (Dremel) with 0.8mm (1/32") and 1.2mm (0.05") drills
    - wet-and-dry sanding paper (grade 1000 ... 4000) or some dedicated cleaning tools (like SenoBloc)
    - etch resist pens with 0.8mm (1/32") and 1.5mm (1/16") tip
    - tray for etching solution
    - etching solution (FeCl3)
    - a thinner (acetone)
    - some additional tools: vise, X-Acto knife, plastic tweezers, board cutting tool (optional)
    - protection googles, rubber gloves

Safety:
    Use protection googles when you drill. When you handle etching solution also use gloves. Etch in well airated place and make sure etching solution doesn't come in contact with any other metal, like aluminium. Other tasks are relatively safe; just pay some attention when working with X-Acto.

Procedure:
    I'll assume you have the layout for the circuit done before you start. First you need to cut the copper clad board to a proper size (leave an inch at one side for better handling with the board, though). You can either cut it with board cutting tool or make a cut into the board with X-Acto and bend it so that it'll break along the cut.
    Now drill all the holes on the board. You can help yourself with prepunched prototype board as a drilling template. Place both boards one on top of other and fix them together (you can hold them with vise; copper clad board should be hold by the excesive part which you left at cutting). Make sure that copper clad board is turned the right way around (so you won't wind up with mirrored board where all traces would be on the component side). Also use only 0.8mm drill at this point, even if that is too small.
    Next step is board cleaning. Use sandpaper to make the copper shiny. Also sand away the excesive copper that holds to the edges of the holes after drilling (if you had used good drills, there shouldn't be any, though). After board is clean handle it only by that excesive part.
    OK, time to draw. Using the etch resist pen draw all connections as on the layout. Use 1.5mm pen for thicker traces (power traces, ground planes etc.) and 0.8mm for normal traces. You can also use 1.5mm pen to do pin pads - insert them into hole and turn it around its axis so you get a nice round pad (the tip of the pen will be damaged in the process so you won't be able to use it for drawing anymore, though). Examine all the traces to make sure you haven't forgotten anything.
    Let's etch! Got your gloves and googles on? Ok, pour etching solution to a tray about an inch high and put the board in with copper side facing upwards. You'll have to constanly rock the tray to speed the etching up. From time to time lift the board with plastic tweezers and check if it is ready. It should take about half an hour to etch the board at room temperature. You can also heat up the solution to speed the process up additionally, but do not exceed 50 degrees Celsius.
    When the board is ready put it under a flowing water to remove the etching solution from it. Dry the board. Now use thinner to remove the etch resist color from the board (if you aren't going to solder the components to board immidiatelly, you can also leave it on as a corrosion protection layer). At the end drill all the holes that are too tight with bigger drill.