Hi Donna,
I hope I can help having been in the 'hospital system' for a few years and recently changing to a new hospital after a move t'up North.
First of all, don't panic. *All* the hospital doctors and staff I've met over the years have been really nice and know what they are talking about - they see KC a lot, be it with lots of different patients or the same patients lots of times
Secondly, take something to read with you. I find it helps to pass the time as you very rarely get seen at the time, or within 5/10 minutes of your appointment. If I don't feel like reading, I just people watch
When you get called in you'll normally have all the usual tests that you've had in the past at your optician and case notes will be started on you. You will also probably have (although I havent had this myself) a test to check the topography of your eyes to show the irregularity of your KC (where the cone or droop are).
If you are suitable for lenses you may well then get fitted with some trial lenses to check fit. These lenses probably wont work for you visually (as in they wont have any power) but they will check the fit on your eyes - fitting lenses for KC can be really hard because of the unusual shape that comes from the KC.
You may be asked at this point to sit for a while in the new lenses to see how you react to them and see how they settle on your eyes. This can take about 20 minutes but differs depending on what lenses you are fitted with.
The doc may then add some die to your eyes (cant remember the name of it) which reacts to UV light so that he/she can check the fitting of the lenses.
If the doctor seeing you can find suitable lenses he/she will then order them for you in the relevant power and sometime in the near future you will be asked back for a fitting.
Note that the first set of lenses the doctor fits you with, even the 2nd, 3rd or 4th may not be the best - its trial and error with KC to find a good fit and everybody is different. What works for me wont necessarily work for you.
As for questions i'd ask everything and anything you want too, and be sure to tell the doc if you are unhappy about anything. Be truthful about comfort too, as it is often is the case that the lenses look great to the doctor but feel like a stick of rock in your eyes - dont be afraid to complain about discomfort.
And for driving home I'd make sure you have a plan b. Generally i've been able to drive home after visiting a contact lens fitting (just end up with sore eyes mostly) but i've started using public transport just in case. Its easier than parking too!
Anyway, hope this helps. Good luck, dont panic and go with the flow.
Ed