How do I make a base for queen size air bed.

How about a kiddie pool that is one of the hard-sided ones.... then fill with something firm enough to support your air bed like tires or strong boxes, cover with cardboard and set your bed down.

For something glamorous get some bender board enough to go around the circumference of the bed 4xs, then get a bunch of verticle boards cut the height of the bed base. Wind a piece of the bender board into your circle large enough for the bed to just sit inside on a bender board lip. Add your verticle pieces to the bender board with a screw so it kinda looks like a sawed off barrel. Add another bender board near the bottom for support using screws on each verticle piece. Add another piece of bender board inside on top of the other one to create a lip. Then add some boards from one side to the other like an old-fashioned bed to be the platform for you mattress - might want to put some old blankets on top to create a soft nest for the air mattress.

or you could make a large square of 4x4s just a few inches smaller than the circumference of the circle, then add planks on top of the square and screw them down, now make a compass from a string with a nail in the center of your platform to mark a circle on the boards, use a jigsaw to cut the platform, then add screw on furniture legs the height you want your platform to be to the underside in the 4 corners.

or you could buy a large animal water tank..... https://www.ruralking.com/tarter-700-gallon-round-stock-tank-wtr82?utm_medium=cpc&utm_source=google&utm_campaign=shopping&utm_content=107657&gclid=CjwKCAjwhevaBRApEiwA7aT53zme3lTpkEOHkL_X7YzRWwkd_JGvfPMQhG4s4FssaxkitiKJR0vvjBoCrYUQAvD_BwE

https://www.youtube.com/watch?v=SJxBlI-x7GU