How I design and make circuit boards:
To design the boards, if I were starting from scratch, I think I’d try to get good at kicad or maybe the geda (GNU EDA) suite because they’re open source, but when I started, they were more confusing and fragile than they are now. All the tools (not just the ones in this note) can produce gerbers (an industry standard file format), which any board manufacturer can accept.
Open source tools aside, Eagle seems to be the standard for little open source hardware projects. (A “Light” version of Eagle is free.) I don’t use the Eagle Auto-Router because it kind of sucks, but it’s good enough for small or low-volume boards or boards you aren’t going to etch by hand, and the thing I do instead is fairly complicated (freeroute plus Sikuli on my Mac). I think on Windows PCs the CADsoft guys are now making it easier to use alternate routers. If you’re making your own boards, it can be worth optimizing or hand-routing your layout if you can avoid double-sided boards and vias. But if you’re getting boards made, double-sided and vias are usually just fine (until you’re making thousands of them).
There is a service in Portland, Oregon, OSH Park which makes excellent boards.
They do a lovely job of taking your Eagle files (or gerbers from any other CAD package), showing you what you’re going to get online, giving you a price based on the size of the board ($5/sq in. for three copies of the board, no setup fees!) then sending you boards in the mail a couple of weeks later. They’re purple and gold, and really well-made. (Holes line up, which isn’t necessarily true of Golden Phoenix or other Chinese boards, which tend to be cheaper for higher quantities.)