To spot it you just need to fly it enough while paying attention to either the sideslip ball instrument, or doing positive and negative barrel rolls to the left and right, without any rudder input. You'll see which way it goes. The problem is the tail is heavy, and there might be some fuselage blanking of the vertical tail surfaces past a certain yaw-AoA, so the tail's free to swap ends.
To stop it from happening you just need to be on the rudders anytime you're doing maneuvers that tempt the tail from swapping ends. If you don't rudder when extremely slow you'll never exploit many of the best maneuvers the 152's capable of.
The safest way to land is to flare it. Keep the RPMs up to help the airbraking, and it won't be any more difficult than landing an F4U. I don't know if flaps could help. If you don't care either way or don't need to rearm, you could just belly it.
To come out of the spin there's no real rule of thumb. Flaps out and gears out help, sometimes. You know you're about to recover when the yaw's slowed down, the wings level, and the nose comes down to the horizon. At that point, push the nose down with full throttle and you should recover pretty much everytime.
What you need to keep in mind when the tailspin's really gotten out of control is that you might be flying backwards, tail first, which might mean (dunno for sure myself) that the controls are inverted.
