For regular rental it's typically per hour the engine is running ("hobbs time", aka the airframe clock which activates off of oil pressure) and then there's often an overnight minimum if you want to take it somewhere else overnight, often 2-3 hours. That means if you want to fly out Friday and come back Sunday somewhere 2 hours away, you'd be billed 6 hours if there's a 3 hour minimum per night (though often minus the cost of fuel, so closer to 5 hours). Fuel is typically included in the hourly rate and is reimbursed if you have to buy any off field.
If you are part of a flying club (everyone buys in for a few grand and own x% of the aircraft) then the rates are typically said to be "dry" and are just the aircraft without fuel and typically billed with "tach time", or the engine clock rather than airframe time which measures rpm / max rpm * time which is in practice about 0.8 * "hobbs" making it slightly cheaper for some operations. Flying clubs vary a lot but are typically more lenient and often don't charge a minimum for overnights as long as you aren't abusing the heck out of it (ie. fly an hour away, spend a two weeks, fly an hour back).
If you are part of a flying club (everyone buys in for a few grand and own x% of the aircraft) then the rates are typically said to be "dry" and are just the aircraft without fuel and typically billed with "tach time", or the engine clock rather than airframe time which measures rpm / max rpm * time which is in practice about 0.8 * "hobbs" making it slightly cheaper for some operations. Flying clubs vary a lot but are typically more lenient and often don't charge a minimum for overnights as long as you aren't abusing the heck out of it (ie. fly an hour away, spend a two weeks, fly an hour back).