At the very least, you will have to make your minimum payment every month. There is no way around this. If you find yourself in a difficult place financially, then remember there are a number of income based repayment plans that you can shift to. Failing to make your minimum payments could negatively impact your credit score for years, which would lead you to a number of other financial challenges. It's hard enough to manage through your student loan debt that you don't want to deal with poor credit as well.
After you make your minimum payments, you may have more cash available and you may be motivated to pay more than that to get rid of your debt as soon as possible. It is important, though, for you to prioritize your student loan payments within the context of your overall life goals. Student loan debt is not like other debts where you can pay it down, but then have the ability to re-borrow down the road should a financial emergency arise. Therefore, before you pay more than the minimum payment on your student loans, consider the following:
1) Is your emergency savings fully funded? – You should have 6 months of monthly expenses saved in your emergency savings account. So if your monthly expenses are $2,000, then you should have $12,000 in your emergency savings account. I always tell clients that 1-2,000 dollar events happen all the time and you don't want to get in financial trouble because you didn't have enough saved in cash to cover them.
2) What near term life goals do you have? If you are planning to get married, or buy a house or have a child, all of these events are expensive and having a healthy cash balance will be critical. So extra money that would be used for paying down student loans should be saved for covering these upcoming events.
3) Do you have debts other than student loans like credit card debt? If so, what interest rates are you paying on these debts? If the interest on the other debt is higher than your student loans, then you should pay off those debts before your student loans.
4) What does your retirement account look like? Have you started planning for retirement? If you haven't, then extra money that would go to student loans, should be considered for funding a retirement account the earlier you start saving, the more you will benefit from investment returns in your retirement savings vehicles.
I know you want to pay down your loans as quickly as possible but you also want to make sure you have enough cash or investments to fund your life events as well. If you have covered all of these items, then you should use extra funds left over to pay down your student loans faster. Your typical monthly payment is split between interest and paying down principal. When you make extra payments, make sure you make those at a different time in the month than your normal payment because the majority of that extra payment will go towards paying down your principal instead of also paying interest. Which will bring down your student loan balances faster.