There is more information about air travel with a wheelchair in post #15 of the disABILITIES FAQs thread (near the top of this board or follow the link in Cheshire Figment or my signature).
Not all airplanes have closets and not all folded wheelchairs will fit in the closet if they do have one. If there is a closet, you have to ask to use it for your wheelchair, they don't automatically put a wheelchair in there. It is first come, first serve, so if you want to check about putting your wheelchair into the closet, ask ahead of time.
For gate checking, as when you check in for the flight. Sometimes they will give you a gate check tag right away; sometimes they will tell you to ask at the gate. Be sure to ask before boarding starts. Also, if you want to preboard, be sure to ask ahead of time. They used to preboard anyone using a wheelchair; some people don't want to preboard, so if you want to/need to, be sure to ask.
You will be able to use the wheelchair right up to the door of the airplane. If she can't walk well, they do have narrow wheelchairs called aisle chairs that can fit right into the aisle of the plane. There are pictures of the aisle chair process in post #15 of the disABILITIES FAQs thread.
Before leaving the wheelchair, you want to remove anything that can be easily taken off (like if you have a loose seat cushion). Those things can be brought onto the plane with you and put into the overhead bin. The wheelchair and any pieces of it you bring into the plane don't count toward your baggage or carryon limit and they can't charge extra for them.
If you are able, fold the wheelchair before leaving it at the gate for the baggage handlers.
As Alan mentioned, even though mobility devices are unloaded and brought to the gate first, it sometimes takes a while to arrive. So, you don't want to be one of the first off or you may find yourself standing in a crowded gate area with not wheelchair and no place to sit.
We have also found that if there are a lot of small children on board the plane, there will probably be a lot of gate checked strollers. These may block access to your wheelchair. So, we end up waiting until most people are off.
If you need an aisle chair to get off the plane, you will be waiting until all the other passengers are off the plane.