How would anarcho-capitalism handle infrastructure?

Mostly in the same way we are handling it now. The difference would be in who's paying for it.

Currently, there is no way for the people to avoid paying for the infrastructure they don't like, and don't use. Environmentalists who are not driving a car are forced to pay for the roads. The poor, who cannot even afford a car, are still affected by some taxes, and a percentage is used to build the roads. Some corporations can be mostly using private railroads, but the taxes collected from them are still used to build the roads. No matter what your circumstances are, you have to pay, or people with guns would drag you to jail.

Under anarcho-capitalism, everything is voluntary. You can't be forced to pay for the things you don't need. Environmentalists are paying for their bike, and the bicycle lanes they are using. The poor ride the bus, and enjoy cheaper food (since there is no taxes, and no regulations, everything becomes cheaper). The typical middle-class family is driving the car, and paying a certain amount for the privilege to use the road, to the owner of the road, but they are still happy - since there is no crippling income tax, a quarter of which is funding the war in some remote region.

What it leads to, is that there would be more of what people need, and less of what people don't need. Say, nobody in their right mind would ever build this wonderful bridge to a tiny island in Russia with the population of only 5k people. It's a huge waste of resources. That bridge is useless. But it was still built, because Mr. Putin did not build it with his money. He built it with money he stole from the impoverished population of Russia. Sometimes, less is more. Building less infrastructure may lead to a better quality of life for the people.