Car won't start

I have a 2003 Pontiac Gran Am it will start once but after that if you turn off ignition it will not start again until it has sat for a long time

Are we to assume that it will crank and crank and crank but won’t fire up?

Or are we to assume that it won’t crank at all? If so, then what will it do? You turn the key and nothing? You turn the key and get click-click-click? grind? or what?

What is typical for one of your drives? Will it do this after 10 miles, but not after a 1/2 mile? If you go out in the morning, start the car and just move it does it also do the same thing?

How many miles are on the car? How old are your plugs & wires? Fuel & air filters?