What kind of flaps are used in gliders?
As Timothy already mentioned, most trainers do not have flaps, but when a glider is equipped with flaps, it would be most commonly in form of flaperons where full-span ailerons are coupled with flap control allowing common-mode motion both upwards and downwards. In contrast to the powered airplanes, flaps in gliders are used not only for landing, but also (maybe more importantly) to adjust optimal glide ratio for the speed currently flown. Thus upward turned flaps are common configuration during fast gliding between thermals for example.

Finding information for particular gliders, especially such mentioning flaperons explicitly turned to be quite hard. Pilot operating manuals usually just describe how to manipulate flaps handle without going into the details on actual construction. Typical placecard for flaps handle (from DG-400 manual) does look like this. Ranging from landing configuration to negative flaps.


Particular gliders equiped with flaperons include (maybe not the most modern ones, but those I was able to find some more info about, good enough as examples IMO):


DG-800 and LS-10 has full-span flapperons. Mentioned explicitly in the flight manual: The wings feature single piece flaperons, which are driven at two places. The mixing of aileron and flap deflections takes place in the fuselage. (The same formulation exists in LS-10 flight manual.)
DG-600 -- according to the wiki.
ASW-20 (and probably some other Schleicher gliders too) -- there are two distinct surfaces on each wing, sometimes referred as "flap" and "aileron", but both of them actually moves according to the mixed inputs of both controls, the ASW-20 flight manual contains nice table of deflections:

Eta has three flaperon sections on each wing, each with different mix ratio between control inputs
... and many others, I believe