It depends on the tour. I use Adventure Cycling maps when they have a route that goes where I want to go.

There are the AC maps I already mentioned, There are also state bicycle maps from the Department of Transportation for many states. The latter are generally free. I also usually pick up a regular state road map as I enter a state, they are often free if there is a visitor center.

It gets easy with practice, but using an AC is a good start in the beginning because they usually list a lot of free places to camp. It helps to choose a well established route. On the west coast cheap hiker biker sites are common in state parks. In the middle of the country you can typically just pitch a tent for the night in just about any very small rural town's picnic area. In the east it is tougher unless you like to stealth camp or are willing to spend a good bit for $$$ camping. Staying with hosts is nice when it works out. Warmshowers.org is one way to manage that, but I usually only stay with hosts who I am invited by after chance encounters.