A spin is a quasistationary state in which the plane rapidly spins around a vertical axis, driven by lift differences between its wings. The spin axis is located close to the nose of the airplane, so its tail and wings swing around. This induces additional speeds on them, increasing the local angle of attack on the receding wing and vice versa on the progressing wing. While the receding wing shows fully separated flow, part of the progressing wing experiences attached flow.
Principle of a regular spin (picture source)
In a regular (steep) spin the angle of attack at the center is between 30° and 60°, and the control surfaces keep some of their effectiveness. A flat spin occurs with an angle of attack well above 60°, so all flight surfaces and their control surfaces show fully separated flow.
Of course you can stall gliders. However, putting them deliberately into a flat spin is rather impossible without specific modifications to them. Part of the certification tests is to enter a spin and prove that this is either impossible or easy to end. Flat spins are very hard to end, so a glider which gets easily into a flat spin will not be certified.
How a flat spin develops and what preconditions must exist for it to be possible is explained here.
When I talk of spins from here on, I mean regular steep spins.
The normal way for entering a spin is to slow down and stall, then kick the rudder hard in one direction. The airplane will yaw and roll and pretty soon enter a spin or a spiral dive.
Some gliders will not enter a spin but only a spiral dive. Due to the much lower drag in a spiral dive, speed will quickly increase and will make this maneuver very dangerous if the dive is not ended soon. For example, the popular training glider ASK-21 will not spin if flown by two people. Flown solo by a light person, it will happily spin and the spin can be ended already if that person unbuckles and leans forward. The small shift in the center of gravity will be enough to end the spin.
In glider aerobatics spins and inverted spins are performed routinely. Inverted spins are started in inverted flight, but otherwise in the same way as upright spins. It is advised, however, to pull out of the spin into upright flight instead of ending the spin inverted. Multiple negative gs are painful!