We just had the Kane Country Treasurer in our office the other day about just this subject. In Kane County, as I'm sure it is in most counties, the taxes get sold 1ce a year at an auction. In effect, you are paying the taxes for that person and they will owe you interest on those taxes if/when they pay you back. As part of the auction, you bid on the interest rate for those taxes...lowest bidder wins.
That homeowner has the right to redeem those taxes...i.e., pay you for the taxes and the interest they owe any time up to 30 months after the tax sale (you may want to check with your local county office to see what their redemption period is). In subsequent years during that 30 month redemption period, if they continue to not pay taxes, you have a right of first refusal on subsequent years' taxes...at a preset, high interest rate.
If and only if they don't redeem will you get the property after the 30 months. Then, there may be legal evictions, etc., that have to take place (which you pay for) before you take possession. And the Kane County Trasurer claims this only happens in an infinitessimal percentage of the cases...almost all are just investments that make interest and receive interest income.
Anyone wanting to invest in tax sales needs to approach it with a mindset that they are going after the interest income they'll receive on the tax money rather than being able to "buy" properties just for their taxes.