Just to let you know what lies ahead....
If you want to go from making a hand-built breadboard or prototype to actual PCB's, you have a lot of hours and anywhere from several hundred to a few thousand dollars cost in front of you, depending on how much you are willing to do yourself.
Schematic capture and PCB layout
First of all you need to capture your design using some sort of schematic capture program, and then design a PCB. One of the more popular programs is EAGLE, which I use. They have a EAGLE Light version ($49), but it can only be used for schematics with one sheet (any size), two signal layers, and 100x80mm (approx 4"x3") routing area. For any serious work, you need at least the EAGLE Standard version, which costs $747. There are probably other less costly (even free) alternatives. There are lots of others that cost thousands or tens of thousands of dollars. In any case you will have to spend considerable time learning how to use the program.
Or you can pay someone like me to do it for you ($$/hour).
PCB Fabrication
Getting boards made is the next step by a PCB fabricator. The problem here is the NRE (non-recurring engineering) costs. Some board houses treat this as a separate figure, and others built it into their per-board quote. In any case, it is almost never economical to have just a few boards made. You might spend $100 for two boards, and $500 for 25. You need to have really large quantities to get down to just a few dollars per board.
The gotcha is, if you make 25 boards, populate just a couple of them for testing and find they don't work (and there is not an easy fix -- e.g. because you laid out a connector backwards), you might end up throwing away the other 23 blank boards away and you would have been better off just getting two. I have stacks of blank PCB's as evidence of this phenomena.
PCB Assembly
Unless you are willing to build the boards by hand, you will need to have them assembled. Surface mount packages are difficult to deal with. If the board has BGA or QFN packages, you probably won't be able to build them yourself unless you have your own reflow oven.
Getting your first two boards built by an assembly house might cost $500. Whereas getting 25 built might cost $1200. (Once again, the problem here is the NRE costs.) Getting down to just a few dollars per board requires (again) large quantities.
And someone else has already discussed the problem of getting parts.
Make sure you use parts that are readily available -- if both DigiKey and Mouser have hundreds of the part available you should be okay. If instead, they have it in their catalog, but it is currently out-of-stock, try to find something else. If you need some special parts that aren't carried by DigiKey or Mouser, make sure you have a reliable source before incorporating it in your product. (Note: the more unusual parts you use, the more likely you will have to add the part manually to your PCB parts library.)
Custom Cases
Do you want to put your board into a case? If you need to have a custom case designed, that will be a couple thou for the designer using a program like SolidWorks (I don't do that, but can recommend someone who can). If you are going to make just a few cases to begin with, you will probably need to go with rapid prototyping, such as Selective Laser Sintering (SLS). Figure at least $100 per case in small quantities. To get down to a few dollars per case cost, you need to have a custom mold made. NRE time again! Plan on spending $10,000 or more for the mold.
And I won't even start on EMC or EMI testing, since I don't know if it applies to your product.
As you can see from all of this, until you get into production, the cost of the electronic parts is usually not the biggest item on a per board basis. Doing your own assembly for small volumes will save you a lot of money. So it is important to design with that in mind -- no impossible to solder-by-hand parts.
To get really low prices for high-volume, generally you need to go offshore -- China etc. But I would avoid doing so in the beginning.
Best Answer
They use a cut tape splicer - this company seems to sell a few, along with the necessary supplies: http://www.tapesplice.com