Little disclaimer: I am not a tax expert and cannot offer professional advice.
The claim that student loan payments are made with after-tax money is not an accurate statement, at least not in the United States or Germany. I would like to clarify this issue, as it may be helpful for anyone who is trying to map out their future costs.
A student loan payment (like most loans) can be split into two parts: part of it pays back the "principle" of the loan (the amount you initially borrowed), and part of it pays back the interest on your loan. Payments made on the interest of your student loan is tax-deductible (i.e. you do not pay taxes for it), whereas payments made on the principle of the loan (called "amortization") is not tax-deductible (the "after-tax money" referred to by usdenick).
The ratio between the two payments is not fixed. Generally speaking, when you start to make loan payments, you are paying more in interest (because the balance of your loan is still so high, so you owe more interest every month). Near the end of the loan, the reverse is true. What does this mean in practical terms? To use the $500 monthly payment example from usdenick, if you have that $500 monthly payment for 10 years, the amount of your payment that you can write-off for tax purposes changes. From a tax perspective, you will be paying less in the beginning of re-payment than in the end. This is helpful if you are taking out a student loan, buying a home, etc. because the burden of your loan payments are lower in the starting years.
For the excel-savvy among you, you can use the IPMT function to calculate how much of your monthly payment would be interest payment in any given period in the loan repayment.