Making a PCB is reasonably straightforward for very simple designs:
Simply follow these steps:
1) Design your circuit
2) Work out a layout for the components and the copper traces between them
3) Transfer the layout to the board
4) Etch the unwanted copper
5) Drill the board
6) Apply components to the board and solder as necessary.
For simple circuits, e.g. a few LEDs, switches and a couple of ICs and discretes, it would be perfectly reasonable to make the board by drawing the traces on using something like a sharpie marker.
For more advanced projects, computer aided design is strongly recommended - this allows you to print the trace layout, and transfer it to the board in one of several ways. With basic software you have to work out the routes that the traces take - more expensive software will route the traces itself. Prices range widely from several $100s - several $10ks.
Making boards with more than 1 layer is very difficult for a home constructor, and making boards with more than 2 is impractical.
Here are a few links about the construction of PCBs, which discuss different methods of 'masking' the traces, and the chemicals and equipment needed to prepare the board.
Link1
link2
link3
link4
link5
link6
If this is all too much, then a very cheap way of getting into PCB design is the service provided by
Express PCB. Download their free software, design the board, and e-mail them the files then, for a small fee, they will send you a completed board. The only catch is that their software only works with their manufacturing process.
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Implementing code on a chip is fairly simple - you need to learn the programming 'language' for the device in question and then buy the appropriate programming kit for the device (prices vary from a $100s - $1ks)
There are dozens of manufacturers of thousands of different programmable chips - it is impossible to give a more specfic answer.
