Not sure about your area, but I'm pretty sure it's common to pay a deposit plus the first month's rent. Also, if you don't have credit or you never turned on utilities under your name before, prepare to pay a deposit and "turn-on" fee.
Read the lease carefully. See if there are any additional fees that you're responsible for. Also check to see if there are any move-out fees at the of your lease. Some management companies charge a bullshit cleaning fee, which is often times ridiculously high.
Also, check your lease to see if there's an escape clause that will allow you to break the lease without penalty, in case you have real asshole neighbors.
Before you sign the lease, walk through the apartment and make a note of any damages. Turn on the faucets and shower to make sure they work, and no toxic brown water comes out. Flush the toilet a few times to make sure it operates properly and nothing is leaking. Check the heater and a/c if there is one.
When you're signing the lease, you'll need to bring the deposit + rent. Some places will accept a personal check. While other places will require a money order. You'll need a drivers license or state ID, and SS card.
That's all I can think of for now.