There are two basic methods, both use gravity, but one uses additional weight.
In this you take advantage of the forces of gravity and the fact that heat reduces the viscosity of glass. The universal belief is that glass tends towards 6-7mm thick. Yes it does, but only under the times and temperatures we give during fusing. Those who have seen the results of relay stuck on for hours will know that glass will become thinner than that. A kiln stuck at 1200C for several hours will produce glass that is less than 3mm thick, although stuck to the shelf.
The practical approach is to give the glass plenty of heat work by reducing the usual rate from bubble squeeze to top temperature. Also increase the top temperature, and give the glass time to flow as it moves slowly.
If your melt is 12mm at the centre and 6mm at the edge you need to take that difference into account when setting the initial rate of advance. A rate of about 90C/hour up to the softening point should be slow enough to avoid thermal shock. You do not need to hurry from there onwards, because the glass needs to be hot throughout to move easily. A rate of 200C, or less, per hour would be fast enough. The top temperature should be set around 810C and for at least half an hour, perhaps an hour depending on the diameter of the piece. Periodic observation is advisable. When the reflections seem fairly straight from one edge to the other, it is as flat as it will get using this process.
Anneal for a piece of 12mm, even though the piece is no longer that thickness, because the glass has been through a high temperature process and the compatibility of some of the glasses may be a little less than originally.
Note that this process should be done on a kiln washed shelf. Thinfire or papyrus will get caught up in the moving glass. The coarser fibre papers will inhibit the flow of the glass. You need to expect to do considerable cleaning of the glass afterwards.
The other method is to use weight above the glass to thin it more quickly and certainly to the desired thickness. Place a kiln washed shelf with the kiln wash facing toward the glass. The weight of the shelf above presses the glass outwards more evenly than a free flow will.
Put solid spacers of the thickness you want the glass to become. Remember that ceramic fibre used as spacers will thin when the binder has burned away. So, a 6mm stack of ceramic fibre paper will be less than that at the end of the firing. The larger the pieces of fibre paper you can use, the less the effect will be, as the weight of the shelf will be distributed over a wider area.
The same kind of firing schedule can be used on the way up as in the gravity only method, but you need to approach the annealing differently. With two shelves and the glass between, you should be thinking of annealing for something in the region of 25mm.
Do not do this pressing on top of your normal shelf, as the temperature differential between the exposed shelf and the part of the shelf covered with 12mm of glass and 15mm of shelf will be pretty large, leading to thermal shocking of the shelf.