I believe that you aren't required to certify hobby electronics, but you still may get a knock at the door if your product is interfering with someone's commercial gear next door.
Certification is required for commercial products.
Certification is also required for anything that plugs into the telephone network.
IANAL (I am not a lawyer), by the way.
There are some other caveats to keep in mind; if you build something powerful that ends up burning down your house or maiming someone, and your insurance provider finds out that it's not 'approved', your chances of getting coverage are likely slim.
If you're tinkering with 5V / 12V stuff at low power, not emitting tons of RF and not polluting the mains, you're probably OK.
I'm no lawyer, but have been thru the FCC testing process a few times. For a ordinary device that doesn't deliberately transmit (called "unintentional radiator" by the FCC), there is no legal requirement for certifcation. There are legal requirements for what it is allowed to emit, but it up to you how to make sure your device works within the rules.
You can simply sell a unintentionally radiating device without testing. However, if someone files a complaint and the device is found to exceed the legal radiation limits, you're in deep doodoo. If you had the device tested by a accredited test lab and they determined it was within the limits, your legal case will be much better. The FCC still has the right to force you to withdraw the product and even confiscate every unit out there, but if you can show you followed accepted practices of testing then there will be much less of a issue of punative actions.
Intentional radiators are a different story. You do have to have FCC certification to legally sell one in the United States. When the device is certified, you get a certification ID, and that ID generally has to be indicated somewhere on the outside of the device where others can see it.
In the case of a bluetooth module, most likely the module vendor has gotten the certification for the module. If not, I wouldn't go near it. Even if so though, you are still on the hook for the product as a whole. The module will also be certified with some restrictions, like a specific list of antennas that it is certified with. If you attach a different antenna, for example, the module is no longer certified and you're on your own.
If you're trying to sell a intentionally radiating product, you'd better talk to a expert early in the process. You can wing it a bit with unitnentional radiators, but you really don't want to play games with intentional radiators, even if you're using a certified module that does all the intentional radiating.
It might be a good idea to talk to a testing house. They generally will know all the rules. Just keep in mind they sell testing services, and their answers may a bit biased towards you needing a lot of testing.
Best Answer
As a rough estimate, the cost is $10k-20k, plus your labor cost.
In the US, all products containing electronics that oscillate above 9 kHz must be certified. The law that governs this is FCC Part 15. The lawyers call this "Title 47 CFR Part 15," meaning that it is the 15th subsection of the 47th section of the Code of Federal Regulations. In Europe, there is a similar regulation called CISPR 22. The requirements are almost the same, but slightly stricter about emissions at certain frequencies.
You can read 47 CFR 15 online. It's not as incomprehensible as you might expect. It seems overwhelming, but if you read the first few PDF's, you'll realize that most of it irrelevant for any single product.
Within 47 CFR 15, there are two classes of testing: Class A and Class B. Class A is an easier test to pass, intended for devices that are used in industrial settings. Class B is stricter, intended for devices that are targeted at consumers.
There is additional testing for "intentional radiators," meaning radios, Wi-fi, Bluetooth and such. There may be an exception if your device is intended for use as a component in a larger system (like a microprocessor or memory card in a PC), but I'm not sure of the legal details there.
The major expense is renting the test chamber. This is what's called an "anechoic chamber," instrumented with a pile of sensors for detecting electromagnetic radiation. To my knowledge, these cost around $1000/hour, and each testing session takes 2 or 3 hours. It's unlikely, but not impossible, that you will pass on the first try.
Here's a decent picture of a test chamber. The one I've been in was actually much larger, like a squash court. I think it was an Intertek facility in Menlo Park, CA.
Unless you're experienced with emissions testing, it is worth hiring an expert, which costs around $500/hour. They can tell you things like, "Put a ferrite bead on that power cable, and that will reduce the emissions at this frequency." The folks I've worked with arrive with a bunch of ferrite beads and inductors (and maybe caps?) of various sizes that you can use in the chamber to hack your device into compliance.
(Perhaps it goes without saying, but I'm an engineer, not a lawyer. I have taken a few products through Part 15, but not in the last couple of years.)
If you're thinking about doing this, start by reading EMC for Product Designers by Tim Williams. I'd avoid the books by Mark I. Montrose; I found them less helpful and more expensive.