Get an accurate picture of your student loan debt by writing down how much each of your loans are worth and each of their interest rates. It might also be helpful to write down each of their minimum payments as well.
Figure out how much you can contribute to paying off your loans right now, then tally up how much you have left over after paying the minimum balances on each loan. Whatever you have left over should go to the loan with the highest interest rate.
Make some cuts to your budget until you can pay off the loan. You don't necessarily have to make sacrifices across the board to save some money. You can save by getting your weekly manicure every other week, making yourself lunch 3 days a week instead of eating out every day, or getting your daily latte only on the weekends. If you're looking to pay off your debts really fast, you can cut your luxuries big time but any way to save money will help in the long run.
Make more money, and use it on the loan with the highest interest rate. You can sell some of your clutter, like clothes that don't fit, on ebay, put furniture or trinkets on Craigslist or have a yard sale and send the proceeds to the loan company.
You can also make money by providing a service - putting in a few extra hours for a couple of months will be worth it in the long run when you have no money going to student loan debt. You could bartend at a wedding, offer to mow your neighbors lawn, petsit or babysit or clean houses.
Once you've devoted all of your extra payments to the loan with the highest interest rate and paid it off, continue making the same payments you were making to that one if possible to pay off the loan with the next highest interest rate until you've paid them all off. Sweet relief!