Are we talking consultation or very first appointment to get them for the first time?
The consultations are basic check up. You're not allowed to purchase any new contact lenses if you're due for a consultation in case your prescription changes. They put a bit of orange dye on your eyes which will show up any scratches. You will also have a basic eye test. Nothing scary. You will be asked to attend wearing your contacts as they'll want to see how they sit on your eyes and then you will need to take them out.
As for the very first time, they will talk to you about how you expect to use your contact lenses and how often. They will advise against going swimming in them and being around people who smoke a lot.
Then they'll give you some to practice putting in after they've explained how. They will also tell you how to tell if it's inside out!
Stay calm, you pull up your upper lid and hold it there, look directly forward into the mirror and gently place the lens onto the eye. It might feel cold and sting a bit but make sure it's pushed onto the eye properly and then blink a few times.
It honestly gets easier as you go.
Don't be discouraged if you struggle at first, I used to have my eyes streaming every morning when I first got them and now it's easy I just pop them in.