Fluorescent light ballast
 

I have an 8-foot, two bulb fluorescent fixture in my garage. When it started acting up (one bulb on/one out) I changed both of the bulbs but there is still one that will not light, it just buzzes. It was there when I bought the house, so I'm not sure how old it is, but could this be a problem with the ballast?

The problem definately sounds like the starter ballast to me. Should always check these before changing tubes. Do you know how to remove and check

It's attached to the housing by a few screws, but how do check if it's good or not?

There will be a small round can shaped starter for each tube fitted into the light fitting, they are normally at either end between the tubes. to remove them you turn 1/8th to the left then pull it out. ( on some fittings they are on the side or the end.) the only way to check if they are faulty that I know of is to swap them from one fitting to the other, then if the other tube now does not light up then you can be sure that the starter is faulty .

I guess that makes sense, thanks for the tip!

Ballast might not have a starter. In that case you just replace the ballast.