Okay at 2 months you would have a surgical abortion. After an abortion they would give you a few pills to take at home. They may give you birth control pills(helps with bleeding after an abortion and normalizs hormones), antibiotics(prevent infections) and methergine.(helps stop bleeding by making your uterus contract back down to normal size) noone has to know you had an abortion unless you get special pain medicine during your abortion, because you cannot drive after being put to sleep. Many clinics like for you to have a ride home anyway because it is good to rest.
*** how an abortion is done.
1) they will put you to sleep if you are able to have the medications.
2) they insert a speculum just like a regular female exam
3) they also insert a tenaculum which hold your cervix and uterus still
4)they clean your vagina and outer labia with antiseptic to prevent infection. (much like other types of surgery.)
5) they will dilate your cervix using small metal or plastic rods. They will dilate it to about the size of a bal point pen.(a bit smaller)
6)they insert a suction cannula and remove the pregnancy.
This is pretty much a basic description of what happens.