Hey guys, my name is Alex and I just recently started riding a bicycle again. An accident kicked me off my bike a few years back and I'm trying to get into the swing of things. Here's my problem.

I bought an old red bike at a flea market for $30. It is a road bike called a Schwinn Caliente. I've been riding it around my neighborhood the past few mornings and I've noticed that every 2nd or 3rd pedaling cycle, the rear derailleur and derrailer pulley are clicking and moving funny. It seems as of the chain is out of alignment or something. Other than that it rides fine, shifters are an acquired taste though, haha. Any help would be greatly appreciated.

Here's a picture of it.

Go to the Park Tool's web site (parktool.com) and read their tutorials on derailleur adjustment.

I suspect a tight chain link. Put your bike in a stand and turn the pedals slowly while watching the chain pass through the derailleur. If it's a tight link, it should become obvious which link is the problem:

Park Tool Co. » ParkTool Blog » Tight Link Repair

Looks like the shimano "Front Freewheel System". Closer pictures of the front crank and rear derailluer area can verify this. It is a completely different animal, although I agree with John, it's likely just a tight link.
https://www.youtube.com/watch?v=vOyiDEFjE5w

Front freewheel - Wikipedia, the free encyclopedia