Bicycle Mechanics - Squeaky front sprocket

On my ride today, I kept hearing this periodic 'Tweet.' At first I thought it was a bird, but no, I believe it is my front sprocket. I notice when I pedal backwards, it makes a pretty loud screeching sound. When pedaling forward, there's a periodic sqeak. I store the bike in a shed in my yard. It's never been rained on directly, but it has been humid in there. The bike is only about 2 months old. Is this normal? Is this something I can easily lubricate myself? Should I take my bike to the shop and let them do it?

Try oiling the chain and see if that silences the squeek. Second, be sure the bolts holding the chainrings to the crank arms are tight. If those two things don't quiet it down, you will need to have the bottom bracket looked at by a shop.

I'll put money on it not being drivetrain-related. Try greasing your seatpost and saddle rails and tightening down the binder bolts.

I'm leaning towards the problem being the chain now. I got off the bike, and rotated the pedals backwards, listening for the squeak. I heard it at both the front and rear sprocket. When I held the chain away from the rear sprocket, and rotated just the sprocket, I heard nothing. I'm going to try to oil the chain a little today. Is there any specific oil I should be using, or is plain old 10W30 ok?

10W30 is fine for your car.
Try bicycle chain lubricant.