A balance transfer can be a great way to get a lower interest rate on some of your higher interest debt. In my experience, the best way to get a cheaper balance transfer rate is to pay off the credit card in full that you want to transfer to. A couple of months after you do that you will get some balance transfer checks in the mail at super low rates - at least that was the case for me and my Chase credit cards.
If you can't do that, you can always call in and ask for a low balance transfer rate.
If this is your plan of attack, make sure that you have been paying on time as it will help your case. Also try to have your other bills paid on time. If your credit report shows that you are making payments on time it will help your case.