There are many brands of hair powder out there, but essentially they all do the same thing. You choose a powder that best matches your hair color, and you either sprinkle it on or use a cosmetic brush to apply it to thin spots on the scalp. It acts as a "mask" on your scalp, basically. Where the pale scalp used to glare out between the sparse hairs, becomes almost invisible as the powder colors the scalp and "blends" the hair in. However, this solution is only temporary. Once you wash your hair (or if you sweat profusely, I would imagine) the powder washes away. But other than maintenance, I've not heard any bad reviews. It gets the job done fairly quickly and easily.
Though I may not have issues with thinning hair, I certainly know the woes of an oily scalp! This stuff will help remedy the oil problem as well. If you didn't know (or if you forgot), powder absorbs oil. All dry shampoos contain some kind of powder - it's what makes your hair appear less oily. But if you've ever used regular dry shampoos, you know that the darker your hair is, the more the dry shampoo will tend to make it appear "gray." Personally, I'm not ready for any gray hair just yet. I use a colored hair powder for my "oilier" days. The brand I like can get pricey, so for a cheaper option, scroll down to the next paragraph. If you're interested in the stuff I use, I prefer Finley. You just sprinkle the powder on your roots or (as in my case) apply with a large kabuki brush.
I've done some scouring, and I've found what I think is a pretty affordable hair powder (depending on how much you use, of course). I'm sure better deals spring up here and there, but for those, you'll have to do the legwork on your own. In the meantime, I've found this one for $9.57 (currently).