Service Dogs can help people with disabilities become more mobile. It may seem intimidating to travel on an airplane with your service dog, but it can help to realize that to the people who work on the airline see passengers with disabilities traveling with their service dogs all the time.Most people call the airline ahead of time and let the airline know they'll be traveling with a service dog (they may put a note on your ticket), but you go through security just like everyone else. Security will inspect the dog's vest and such, just like they would do with people. The procedure varies, but often the handler walks through the security booth, leaving the dog, then calls the dog through, and then the dog is directly inspected by security. Sometimes the TSA does a hand swab on the handler, too.
When you arrive at at the gate, you'll board with the dog, and then go to your bulkhead seat, which gives you a little more room at your feet. Some handlers with a service dog prefer to buy "stretch seating" or "economy comfort" so they get the extra room a bulkhead seat would provide, but also get the under-seat baggage room (this option costs money, but some handlers find the extra cost worth the expense). The dog then lies at your feet during the trip. The goal is to make everything as easy as possible - many passengers and flight attendants often don't even realize there was a dog on board!
You will probably feel more secure bringing paperwork (doctor's notes, the dog's service dog graduation certificate, immunization records), but the airline often doesn't ask for any of this paperwork. Optional: Many passengers find it helpful to have medical documentation as a way to discreetly communicate information about their needs to security, and so the TSA has created a Notification Card that passengers can use for discreet communication. Use of this Notification Card, or of medical documentation, does not exempt a passenger from screening, but the card can be a nice reassuring way of smoothing out situations.