I'm sure I need a light bulb of some type, but I do not know what kind or what else I need. I just bought my first house and I am a DIY rookie.
The holes in the white part look like they might fit a G4-base halogen bulb:
It also looks like there is a label that's curling away from the side of the fixture in the lower photo; if so, it should have information on the maximum wattage that you can use.
It's hard to tell from the picture if the lens assembly includes a reflector. If it does, Niall C's answer is probably correct. If not, an MR16 bulb includes a reflector and a similar bi-pin base. Both types of bulbs are used in low-voltage landscape lighting.