What's wrong with my battery?

So I've recently been having a problem with my car battery. It starting acting up last week. My battery light came on and both my headlights and interior lights got really dim. The first time this happened I was experiencing this problem and just happened to roll through a puddle of water and everything went back to normal. What does that mean? Well the next day I bought a new battery and the problem seemed to go away, but no. Just yesterday it started doing the same thing again. My friend told me that it's probably a short, but I don't even know where to start looking. Luckily I've got a waranty on the car battery so I'll replace it, but I don't want to have to keep doing this every week. If anyone has any ideas of where the short might be or what the problem actually is, please help... Thanx

Alternator, corroded battery cable.