Building and Driving a Stepper Motor
You can drive a small bipolar stepper motor using an L293, SN754410, or L298

If you find a unipolar stepper motor (not uncommon in the paper advance on cheap printers) you can drive that relatively easily with discrete NPN transistor switches.  In theory you can do a bipolar motor that way, but the circuit is a bit trickier (it's easy to get both the high and low transistors on and as a result short out the power supply, making them rather warm).  Besides printers (copiers?) floppy drives are another salvage source, but hard drives switched to voice coils ages ago.  Lots of surplus outfits will sell you motors; if you aren't looking for something powerful enough to run a machine tool you probably won't have to spend much.

Since you are very new to embedded programming as well, you might want to look at one of the "motor shield" type solutions - not necessarily to buy (though of course that is an option) but to study the plans and example software.

If working with a salvaged motor for which you don't have data, start with low voltage/current until you get movement.  One thing that can be interesting to do is to take a &lt;1 amp power supply and work out the series of voltage applications to the winding by hand connnecting them to slowly step the rotor.  You can buy chips such as the L297 which generate this sequence to control the power driver chip, or you can do it yourself in software.

Actually making a motor may be fairly tricky, but people do make brushlesss motors which are stepper's lower-pole-count cousins.  For early experiments ball bearings are likely not your greatest concern - plastic or oil-impregnated bronze sleeves might serve.  But rollerblade wheel bearings are fairly cheap: mounting them is going to be a big part of the challenge (and a challenge which starts to stray from the topic of EE stackexchange)