There are a lot of ways to build and design a board yourself. Certainly any of the free tools, Eagle being one of them but the are many others that can get you where you need to go. There's a bit of a learning curve as you will have to define the symbols for the part(s) you are using, then create a schematic. From there you need to create the footprints, or the physical drawing of what the part will look like on the board. Place those on the board and then route your signals and gnd between them. I'd suggest looking through a tutorial on how to make a simple board with whatever tool you pick.
If you're going to send these out to a shop it pay attention to the design rules the shop has for the cheap price you likely want to pay. You can't just make lines and spacing anything you want. Often the cheaper the price the larger the spacing, the larger the holes etc.
To actually make the PCB there are many options. You could print and etch it yourself, heck there have been times when I've carved one out of bare copper board with an exacto-knife. If you're going to have it made at a shop then start looking around at prices. I've seen prices as low as $10 for tiny protos of a few 2 layer boards (with a little waiting time), but keep in mind what I said about verifying their capabilities.
It's probably a worthwhile learning experience to make your own board but it is more work than you maybe suspecting.
One last thing the last time I saw an accelerator breakout board it was a little smaller than a quarter. If you're going to make something smaller than that you might want to add some break out tabs and maybe put a bunch of them on a single pcb.