As for what the actual procedure was... this is what happens at my doc's office (family physician, not a ped):
We do weight on a scale outside the room, then go into the room for a length measurement. I then take of her onesie (don't put anything fancy or difficult to remove on either baby (or yourself) since you could get something on it) and diaper and the nurse does the rectal temp. She asks if I have any specific questions for the doctor and writes them down. When the doc comes in he does a physical exam, checking for neuromuscular disorders and internal abdominal organs and hernias. Don't freak out about these checks -- they don't hurt baby.
He does a quick check of the genital area and then answers my questions. He plots her height and weight on the CDC charts and goes over relevant feeding, developmental, etc. issues for the next few months. He leaves and the nurses come in to do the shots.
I had hoped to be able to hold her in my lap while they did them, but I was told no. I had given her Tylenol in the waiting room to help with pain. One nurse helped steady her (as did I) while the other did the actual injection. 2 in each leg, IIRC. Baby screamed like I was poking her with hot branding irons for about 15 seconds, but quickly calmed down. Bandaids were applied over the injection sites and I noticed a very tiny amount of blood on them when I took them off later that night.
After the 2 months shots she slept more than normal for a couple of days. After the 4 months shots she did the same, but also ran a little fever and was irritable. No problems after the 6 months shots.