DISCLAIMER: I am not guaranteeing a win. These are simply tips on bettering your chances of winning! I found these tips and since then I've won numerous tickets to concerts, movie passes, etc.
First off do your research. Know what stations are having contests and at what times!
Grab a phone! It can be a cell phone or land line. I've been told landlines work better due to a direct connection to phone lines. I always use my iPhone!
Either have the radio station number memorized, saved in your phone or written down in front of you! This will make it faster when calling!
Radio stations have a little lag between real time and the time they play on the radio due to editing and preventing vulgar things being aired.
Due to the difference in real time start calling a minute or two earlier! The trick is as soon as you hear a busy tone hang up and redial. Keep doing this until you get through.
I know for the iPhone the quickest way to redial is to hang up and then double tap the green call button. I will dial the last number entered.
This green button! Double tap it to redial! It makes it quick!
So keep dialing until either you get through and win or they have chosen another winner. There is no guarantee of winning but it's fun and if you have spare time you can get some great stuff!
A few last things to try, supposedly if you get through and lets say you are caller 3 of 10, don't hang up. A radio station doesn't disconnect you they simply put you on hold.
If the DJ is moving fast they might open your line up and you could win! Also another cue to start calling is when you hear the Radio hosts voice start talking.
Good luck and hopefully you get a win!