I've never made a dovetail joint before, and I'd like to do things right for my next project. I have the router and table and all that - but I don't have a dovetail jig. The prices vary from $40 to well over $400. Do I need to buy a special jig, or is there a way I can just buy the router bit for $10 and make my own template somehow?
If you are using a router you will need some sort of edge/jig to guide the cut, otherwise you won't get a straight line. In the first instance I'd buy a cheap(ish) one and see how you get on. Then if you want to do more advanced pieces buy a more expensive jig.
BTW I learnt to do dovetail joints with a dovetail saw and mallet & chisel. You can use a mitre saw, but a dovetail saw is finer.
Here's a good tutorial on hand-cut dovetails. There are two schools of thought - pins first and tails first. It doesn't really matter, it's more about how you were taught. This one is pins first.
Without significant care, a homemade jig won't allow the pieces to mesh properly when you're finished. Commercial jigs are accurate down to hundredths or thousandths of an inch, and it's unlikely you'll get the same level of accuracy. That said, as ChrisF mentioned, commercial jigs and routers are a fairly modern invention but dovetail joints are not. So using your own jig you may need to do more manual work to get them to fit.
As my father (a professional carpenter for about 40 years) noted, "a 'master carpenter' is just a carpenter with enough experience to know how to hide his mistakes."
I personally cut them by hand (with a dovetail saw, $10 at Sears, and chisels) which is pretty quick for one-offs (no setup really required) and doesn't require any special jigs. If you look up handcut dovetails on YouTube you can watch some people do it and decide how easy/hard it looks.