I did a mixture of paying down the card with the highest interest first and transferring balances. After college I was swamped with debt and the monthly payments were killing me.
Finally, after reading about personal finance, I began paying the minimum payments on everything except the highest interest card.
While I was doing this I found an offer for deferred interest for 21 months! I transferred the highest interest card onto the new card and began chipping away at my debt.
You can find a card like I did by going to this website!