I didn't get a mile from the house on my maiden voyage of the bike I just bought (used), when I heard a snap and a tinging sound. I stopped the bike and noticed that I had snapped a spoke on the rear wheel. I managed to get it home and saw that of all the spokes on the wheels, this one would probably be the most difficult to replace. I'm pretty mechanically inclined, but is this something that would be best done at the bike shop? In all my life of riding bikes, this is the first time that I broke a spoke....

The cassette or cog(s) probably just needs to be removed.

Yeah, judging from what I see it would have to be removed to put the new spoke in. How aggravating is it to true the wheel?

It's not all that bad. Maybe 5-15 minutes to tension the new spoke, once you get the same-length replacement spoke and have the removal tools to get the cassette/freewheel/cog (whatever it is you have) off. Provided the wheel didn't get more out-of-true after the spoke broke, it should be pretty easy.

Just googled spoke repair and it looks pretty simple. Maybe while I'm at it I'll build a jig for truing wheels

Removing the rear cogs requires a special tool (or 2).
Replacing a spoke is pretty easy.
Truing a wheel takes a little practice but is not too difficult. I have done this by the roadside several times. You have to balance trueness of the rim with spoke tension (adjusted with a spoke key such as Spokey). You dont need a rig, you can use the brake blocks to guage trueness.
If you need the bike back in action quickly, get it done at a bike shop. In the meantime look for an old front wheel that you can practice on.

Also, if you just replace the one spoke and tighten it up to where it was before it snapped, the wheel will probably be reasonable true. However, this does nto address the reason why the spoke snapped int eh first place. Most spokes break because the wheel was built with insufficient tension or not properly stress relieved, which allows the spokes to de-tension themselves as you ride. It is likely the whole wheel should be re-tensioned before you call it fixed. Also, since spoke breakage is generally a fatigue failure, there are likely other spokes on the wheel which are also close to the breaking point.

Replace the one broken spoke, bring all the spokes up to correct and even tension, and if another spoke breaks after riding for a few days or weeks then it is time to re-lace that wheel with all new spokes.

since you need to buy a single spoke anyways, you might as well have the shop install it and check the tension.

Yup. It's like adding anti-freeze when your radiator runs low. That'll keep you going for a little bit longer but you haven't fixed the problem.