There is no just one way, but I always weaned 'cold turkey'
I also always had several foals, so they were weaned , having their peers as company and as playmetes
I have safe stalls, with rubber matts, and would put two foals together in each stall, while the mares were turned back out with the main herd.
Those mares would come up to the gate and whinny for the first 2 to three days, then would not bother to
The foals also would settle down after the first day,I then would start to halter break them, first leading them in the stall, then up and down the barn isle, and by the end of the first week, they would be leading out to a corral, to spend the day, then led back in ant night
After about two months,\i would turn them out in the weanling pasture, for over the winter. That pasture shared a common fenceline and stock waterer with the main herd, and it would be the dams of those foals, which would give them the ;loudest get lost signs.
That maternal strong bond breaks rather quickly, once that mare has dried up
Since I fed my weanlings diffrent then the rest of the horses, they spent the winter in that pasture, and joined the main herd in the spring. I only brought them in during the winter, for foot trimming, learning to stand tied, ect