What happens during a contact lens fitting? Can I drive afterward?

I have an appointment for an eye exam/contact lens fitting (first timer!) this Saturday morning, but I have to drive to L.A. right after…is this safe? I live in Santa Barbara, about 1.5 hours away…

Also, what exactly happens during a fitting? Does it hurt? How long will it take to get my contacts? Thinking about ordering through 1800Contacts.com..