Hern puts it well, regarding the chute. Once you've committed, you really should try to turn your brain off and just let the staff do what they do best. I think the most unnerving time for me was the few hours leading up to the hospital and the waiting room. Once in the prep area, they'll give you a cocktail of drugs. Surprisingly at Swedish they did not give me any benzodiazepenes (Valium, Xanax, Atavan,...), just a dose of oxy, celebrex , and a few other things. I asked about all that and they said the oxy generally cuts the nerves pretty quick. Indeed it did.
Maybe I'm generalizing, but I think most staff who work in an OR or prep/recovery capacity are really super friendly, and exude confidence, and they understand that the patient is pretty damn nervous about the whole deal.
Once in the OR, depending on your form of anesthesia, you'll either quickly fall asleep under a general, or if you do a spinal, you may be asked to assist the staff by helping get yourself situated on the operating table, which is followed by a pretty quick-paced prep for surgery, by clamping you in and so forth. As soon as the spinal is set, you'll begin to feel numbness in your legs and hips. They might poke at you to see where the numbness is. In addition to the local numbing they use, they'll also put in a benzo which they'll use to make you hover below consciousness. The anesthiosologist may actually be talking to you and letting you know what's going and I suspect for most folks, when they say, "now I'm going to put in something that will make you sleep", you'll be asleep before you know it. You'll probabaly stay asleep for the duration. Depending on your body weight and probabaly a bunch of other factors you may "wake up" here and there during surgery. Keep in mind that at high doses of the benzo you have absolutlely no anxiousness whatsoever and the lower half of the body is absolutely numb.
Also, before surgery you meet with the anesthiologist and they're in the OR by your side the whole time. You can generally chose which form of anesthisia you want. I'd go with the spinal, quicker recovery with less sickiness.
At least that's how both of my surgeries were. Probabaly some variation among different hospitals. Don't worry about it. You'll be fine.