At work we got a Makerbot Replicator 2. I was excited to have access to a printer, but a little unsure where to get started having no experience with 3D. A lot of co-workers started downloading/printing models from thingiverse.com. It's a nice site because there are tons of cool models you can download which are ready to print. It's a great way to start using the printer out of the box, but to me actually creating a model and printing it is way more interesting.
After some googling, eventually I found Tinkercad. It's a browser-based (WebGL) tool that lets you create simple 3D models. The basic idea is that you have a bunch of primitive objects (sphere, cube, cone etc...) that you can add to a stage and combine to form more complex objects. You can also do subtractive operations. For example, if you wanted to design some dice you could make a cube, and then make some small spheres and subtract that space to make the various 1-6 dots on each face of the die.
Anyhow, my first experiments have been with chess pieces since they have some fairly simple geometry (besides the knight). Here is an example rook I designed.
Once you are done with your model, you can select "Download for 3D Printing."
This presents you with a menu giving you file format options:
.STL is the best option for Makerbot since it doesn't print in color. In case you were wondering.
STL is also known as Standard Tessellation Language ...
... STL files describe only the surface geometry of a three dimensional object without any representation of color, texture or other common CAD model attributes.
Once you have your STL file, you can import it into Makerware - a Make desktop app that lets you adjust how the model will be printed (think of it like the print preview dialog when using a paper printer). Once you adjust the settings you have to export a file which essentially turns the object into a set of instructions for the printer on how to create the object.
Below are some printed models I created with Tinkercad, and printed with the Makerbot Replicator 2:
Taking it further
If you love your model and want it in a more durable format than PLA (the plastic Makerbot uses), try out Shapeways. You can upload your model, get an estimate of how much it would cost to print in other materials such as stainless steel, ceramics, silver (or other varieties of plastic).