ang,
You'll find some descriptions of the transplants of forum members in our
Transplants forum.
I can give you a general outline:
You'll have a certain number of days of chemo, to destroy your diseased cells, essentially removing your faulty immune system. They may then have you wait a day or two before the next step: the transplant itself.
Meanwhile, your brother or sister will receive injections of Neupogen or a similar drug, which causes stem cells to move from the bone marrow to the circulating blood, where they can be easily extracted.
On the scheduled transplant day, you'll be given the stem cells from your sibling. It's just like getting a transfusion.
Then comes the phase where you wait for the new stem cells to move into your bone marrow and engraft, i.e., take over and become your new immune system. You are at high risk for infection before and soon after engraftment, until your white cell count builds up again, so they will keep you as protected from infection as possible. You may need blood and platelet transfusions until those counts rebuild too.
Side effects vary quite a bit from patient to patient, e.g., very sensitive gums, loss of hair, nausea, and other discomforts that will be dealt with symptomatically as you begin the recovery phase. The biggest risk is graft rejection, but that's less likely with a sibling donor. If that does happen, a second transplant might be the backup plan.