Hey Jessica,
I was put on prograf as my antirejection and that can be given sublingual. The rest of them are IV initially. Once you are able to eat and drink again, you will switch to pill form of your meds. They checked my med levels every morning and adjusted the dose almost every day. It takes a while to get the dose right, in fact my dose still changes frequently.
As for getting a dose prior to surgery, I am not sure if I got any. I was only at the hosptial an 1.5 hours before my surgery and I was only in a room long enough to sign consent forms and have my blood drawn. It is possible I got some after I was sedated.