Aluminum sliding doors should be very similar to painting gutters. Both are often made from extruded aluminum, and then painted.
What you'll want to do is take the door and clean it thoroughly. Not just a pressure wash but actually clean it with a cloth and soapy water, and then rub dry or air dry it. Make sure there are no drops of water on it anywhere in the seams or cracks or crannies or whatever else you want to call them.
Next, get yourself a spray can of aluminum primer paint. Just make sure that whatever paint you are using does not contain ammonia. This will oxidize the aluminum and make the paint swell and bubble. My understanding is that Rustoleum makes a primer available at Home Depot for this purpose.
Finally, once the primer has dried, you can go ahead and coat the door with the desired color paint. One website I reviewed mentioned that they recommend having the door painted within 24 hours of putting on the primer, as it apparently bonds better that way.