You start with an idea (whether a clever gameplay mechanic, a great theme/story for the game, or a set of personal goals to build a game around) and have to flesh it out with a game design document. The more detailed you can be in this document, the better you'll be able to answer questions for all the special cases that players will inevitably discover. This document will also help flesh out how the game will actually play, what systems/parts/player interactions there are and how they will all work together. This document will most likely be in a constant state of flux as you develop the game since something that sounds good on paper may not actually be fun to play.
Once you know how your game will work, you'll have to start building the components that make up the game. Assuming you have already fleshed out all the various components needed for the game, you're going to have to figure out how to get or make all those components so you can actually build the game. For counters, tokens, pawns, or other random game pieces, I like to go to Michael's and get bags of small wooden items (stars, circles, button plugs, etc.) or get mosaic tiles. If you want to go a little more professional, Fantasy Flight Games has some good sources for tokens, plastic or wooden.
Chances are good that you have a custom board, tiles, or cards that you need for your game. I use an open-source program called Inkscape to design the sizes of my components, what information goes on them, and what art goes on them. If you're a graphic designer or artist, then finding the art will be easy! Otherwise, you can scour the internet for images to use. Make sure that you have permission to use the images if you plan on keeping this art past the prototype stage. I like to use a filter in Inkscape on all the images I use so all the pieces have a consistent look them. If you don't want to have art in the game for prototyping, you don't need to , but it will be much easier to get people interested in playing your game if it looks nice and at least semi-professional.
Once you've got all the images/designs for the components of your game, you'll have to organize them all so you can print them, and then get ready for some arts and crafts! At the very minimum, you're going to have to cut what you printed into all the separate parts. If you want your board and tiles to feel closer to professional quality, I like to use illustration board from Michael's. It's thick enough to feel sturdy, but still easy enough to cut and fold. However, since that won't fit in a printer (at least not my printer), you're going to have to somehow stick your printed designs on to that board. So that means glue, tape, or sticker paper.
I'm still learning how to build a better prototype and will keep refining my methods to save on time and money costs, but when I started this, I definitely didn't think most of my time would be trying to just build a single prototype to play. And once the game is solidified, I need to get final art, then get a professional prototype built, test it repeatedly, and then start trying to actually sell the game. I've got a long way to go...