Nothing like a new camera to make you feel smart as a box of rocks!

[RhacHead]

I think I understand that there are different modes for the auto focus to work in, so I probably had it set in a wrong mode and just need to figure out which one I want and how to change it.

Sounds like it was set to automatically pick what the camera deems as the best AF point. If Nikon is set up anything like Canon then there will be a button near the mode select dial that will allow you to assign the AF to one of the 11 points that the D3000 has. Try and look up this feature in your manual or ask the seller where its located on that particular camera.