Every procedure will be different depending on the type of abortion, length of gestation, and mental health/certainty of the woman.
I imagine the process is variable depending on the medical facility but in my own experience this is the gist.
You call in to the health center, they book you an ultrasound. You go in, fill out paper work and then have your ultrasound (it's not like a normal ultrasound, you don't see or hear anything) after the ultrasound you meet with a nurse/social worker to have a consult. During your consult you discuss your certainty of the abortion, how far along the pregnancy is, your options for types of abortion, your mental health, your support systems, and birth control options etc.
There are two types of abortions most commonly done, medical and surgical. Medical is most successful done before the 8th week of pregnancy, surgical is the only option past 8 weeks. There are late term abortions but these are RARE. The medical abortion involves a shot in the office and the insertion of medication vaginally at home 3-4 days later, you dilate, cramp and abort. It is painful but usually doesn't last too long. You have to physically check the tissue, if you pass the correct tissue you rest and the procedure is done. The surgical abortion is a bit more complicated. It involves a day at the hospital, you are given medication vaginally to dilate the cervix and then are told to wait. After you are dialated you are given an IV with antibiotics and fluids. The producer involves the insertion of tube into the vagina/uterus and the removal of the foetus (to put it plainly). Recovery is a bit slower for this procedure.
So that's the cut and dry what it's like. If your talking emotionally/mentally, that's a whole different ball game and very unique to each person.
I hope this isn't a huge jumbled mess!