Libertarians don't want no government at all, they just want the minimal amount of government necessary to enforce their platform. The people people pay for it, likely in similar ways to how they pay now.
Yes, or in some versions of libertopia you simply pay for what you use. Need a contract? Pay a contract tax stamp that pays for the courts to adjudicate the contract as necessary. Need to drive on a road? Pay a toll to drive on the possibly privately run roads (in any of the various ways that driving tolls can be collected).
This approach obviously has some problems to be overcome, but the idea that people are currently made to pay for things they don't need or don't use just because a majority of their neighbors want them to has problems too, like fairness.