This Instructable is intended to give an overview of the 3D printing process, using a holder for toothbrush heads that I designed and printed as an example. The process is a little bit complex these days (it should get simpler in the future), but this Instructable should give you a good overview of how it works.
Step 1: Measuring
The first step, even before you design the object, is to measure everything. I use a measuring device called a micrometer caliper, the metal tool shown in the photo. You can get an inexpensive one from Harbor Freight for $15-$20, or spend hundreds of dollars for a high-accuracy one. I got mine a decade ago for about $30. It makes measurements simple that would be almost impossible with a normal ruler, so if you are designing, I recommend you get one.
These days, everything in 3D printing is geared toward metric, in millimeters. A millimeter is roughly 3/64 of an inch. Once you get used to using millimeters, you'll find it's much more convenient than counting fractions of an inch. My advice: just go with it.
Step 2: Design
Once you've made your measurements, you need to create a 3D model of the object. In the future, I expect manufacturers will provide 3D models of accessories on their website, but we are not there yet. Today, you need to design your own.
I used a commercial program from Alibre to create the model, but there are a number of free programs. The one from Autodesk, called 123D, has a rich feature set. Blender is open-source, and some like it, but it was really designed for creating objects to be used in 3D animation. There is even a simple modeling program that runs in your browser called 3D Tin. None of the ones I've used is as intuitive to use as I think it should be, but they are getting better.
The Alibre modeling program has some nice machinist features, like being able to extrude a shape and put rounded corners (fillets) on any edge, even a curved one.
Once you have created your 3D model, export it to a file in the standard STL format.
Step 3: Create a Tool Path
The 3D printer is not smart enough to print an object directly from the model, despite what you see people doing in TV shows. It needs a "choreography" that specifies each movement, and when to start and stop pumping out molten plastic, and at what rate to do so. You use a separate program to generate the tool path from the model, which is usually specified in a standard language for CNC machine tools called GCode.
I used Makerware, a free program from Makerbot that is only intended to create tool paths for Makerbot 3D printers. If you are using another brand of printer, you can use the open-source program ReplicatorG. It allows you to do things like moving the part so it is not floating up in the air (which will have a guaranteed failed build) and centering it on the build platform, or scaling it to make it larger or smaller. The output of this program is another file.
Step 4: Print!
Once you have the GCode output file, you need to get it into the printer. Some people have a USB cable going directly from a computer into their printer, but I use an SD memory card to transfer the tool path to the printer. The Makerbot Replicator 2X I use has a small LCD display and buttons that allow me to choose various options, and does not need to have a computer connected.
Step 5: Error!
If you do 3D printing for any length of time, you'll make a few, or even more than a few of these. The holder I was printing came unstuck from the building platform during the build, and as a result was carried around by the extruder head as a rat's nest of plastic strands was output.
After this happened, I looked on the Internet to remind me of what I could do. There were two suggestions. First I increased the temperature of the heated build platform from 110 degrees to 120 degrees, and next I was reminded never to open the door during a build. Cold air currents can cause the object to separate.
I print with ABS plastic. ABS is more error-prone during printing, but once the object is printed, it is more durable and less temperature sensitive than the other material often used in 3D printing, PLA.
Step 6: Prototypes
You will likely go through several prototypes before you end up with a final design. My final design was the third one I printed, and is the one on the right in the photo. I originally made the pins too short, and the toothbrush heads were not stable on the holder.
Step 7: Finished!
Caution: when you get the final version, and actually put it to use, you will be inordinately proud of it. Don't worry; there's nothing wrong with you. It happens to all of us.