The pregnant mare horse will probably lie down though it may stand.
The contractions will come. These can be painful.
If the horse has given birth before it will be easier, but if this is her first time it might prove to be harder.
She will start to push the foal out with the contractions. Eventually if all goes well she will give birth to a healthy foal.
If she is having noticeable trouble, CALL A VET. In fact, you should always have a vet on the scene once the mare starts pushing.
If you reach a hand in the mare's rear end and feel hooves, like, RIGHT THERE, than that's a breech birth. That is an emergency, always have a vet. If you feel the foal's head when you reach in, all is probably well.
Now, understand that the pregnant mare is probably in pain. Soothe her. Comfort her. Pet and stroke her. Be prepared for a long wait until the foal is born.
I repeat, always always always have a professional veterinarian on hand.
There is no special term for a horse birth, although it can be called "foaling."
Foaling. Foaling.
Foaling Foaling
Foaling.
Ideally, foaling takes place in a specially built large stall called a foaling stall. When foaling outside in a herd, mares often separate themselves to foal. A few seek out the company of a special horse friend (usually another mare) or the herd while foaling.
Foaling
No
foaling
Foaling
Foaling.
Post foaling, the mare's uterus needs to discharge remaining fluid and return to it's original size (involute). By around 10 days post foaling the mare has gone through foal heat and completed the "cleaning stage".
Usually not...horses, (like most birthing animals), are calm during the foaling process unless there are significant problems with the birthing process. Much of this is mediated by the hormones released before and during labor and foaling. If the mare has a malpositioned foal (dystocia) the veterinarian may administer drugs that make it easier to reposition the foal. These may include tranquilizers and or muscle relaxants.