Buy a blank PCB, copper-clad on one side. 150mm x 150mm (6" x 6") is good for one board; 300mm x 300mm is good for six boards. (Buy in bulk and save!)
Laser-print the PCB artwork on a sheet of press'n'peel film. You can just barely fit three per page. You must print on the correct side of the film -- if you don't know which side your laser printer prints on, then mark a sheet of paper on one side with a pencil, then manual-feed it to the laser printer, to figure out which side gets printed on.
If you don't have a laser printer, print onto paper with your inkjet printer or whatever, and then use a photocopier to put the image onto the press'n'peel film. But a laser printer is more desirable -- photocopiers tend to randomly stretch/compress the image a bit in one direction.
Lay the film face-down on the copper of the PCB. Lay a sheet of paper on top of the film. Iron. Iron some more. Iron some more again. The back of the board should get too hot to touch. (Make sure you have the board laying on someting that can take the heat OK.)
The press'n'peel instructions tell you how hot to go, and give you instructions as to what to do if you had the iron too hot, or ironed too much. I've yet to manage to go too far, so I suggest you err on the side of too far, rather than on the side of not enough.
Peel the film. Watch carefully as you do: if you see some black staying attached to the film, that's a bad thing -- lay the film back down on the PCB, and iron some more. Peel again -- if that bit of black still stays stuck to the film, then further ironing will not help, so just keep on peelin'.
Don't throw the film away just yet. Get an etch-resist pen, such as a Dalo pen, and look for black bits on the used film. Find the corresponding bit of missing black on the PCB, and colour it in with the etch-resist pen. The reason that you're looking on the film, then finding the matching spot on the board is that it's easy to spot black on the used film, but hard to spot absence-of-black on the board. You may have to press quite hard with the tip of the etch-resist pen to get ink to flow.
Etch. I use ammonium persulphate. I buy in 500g jars, and half a jar is plenty for etching one board. You need a container to etch in: you can buy a purpose-designed etch tank, or you can use an Australian ice-cream container or a plastic chinese take-away food container, or whatever. But use plastic, not metal. Heat your water and dissolve the etchant in it; and then dunk the board in it. As bubbles form, brush them off with an old toothbrush or something, or by lifting the board out of the water and dropping it back in again. Bubbles are bad because the part of the board covered by the bubble is not exposed to the etchant.
If the etching reaction slows down, it is because the etchant solution has cooled down too much -- chuck it in the microwave for a minute or two. Yes, technically we're putting metal in the microwave, but because it's comletely surrounded by electrically conducting water, this is OK.
After etching is complete, pull the board out and run it under some clean water. Then scrub the black off with steel wool. You can get non-steel scratchy pad things for doing your washing up with -- they're plastic and are usually green. These work, but are way more effort than steel wool.
Now drill the holes. Mostly you'll be wanting a 1mm or even a 0.8mm drill bit; a few of the holes, like those for the screw-down terminals, may need to be slightly larger: 1.5mm or even 2mm. The holes for the power socket (if you're using a PCB-mount power socket) may need to be much larger: around 4mm.