Painting vs. Cleaning
The first move is to decide whether you need to repaint your grill. Stainless steel grills and most enamel-coated grills do not need to be repainted. It is possible to paint black painted grills, but it may be that your grill just requires a good cleaning and not a full painting job.
The black painted grill's number one enemy is not rust, it is oxidisation. You might have an oxidization problem if your grill has a dull, ashy look to it. This does not mean that your grill needs to be repainted. With kitchen detergent and hot water, try cleaning your grill thoroughly. Stop something too abrasive, so rather than just washing it you'll scratch the finish and need to repaint your grill. Lightly coat the affected areas with cooking oil until the surface has dried. This will help seal the surface and restore your grill or smoker's appearance.
Your Barbecue painting
It is best to do the whole body of the grill if you are faced with a paint job. A good wire brush or steel wool, metal sandpaper, and barbecue paint will be needed. Paint must be resistant to heat and able to withstand temperatures above 500 F/260 C for grills and smokers. Some people use engine paint on their grills, but you should not have any trouble finding paint specifically designed for grills.
Start by painting your grill, as the paint will repel any grease on your grill. To degrease the grill, you can use an oven cleaner. Oven cleaner is bad for the paint job, but that's not a problem because you're doing this phase just before painting. Notice that to make the painting simpler, you should disassemble your grill. You're not going to paint the interior, so you don't want your burners to be white inside.
Scrub down the surface by means of a wire brush or steel wool. You may want to go over it with sandpaper to get after any rusty areas until you have it washed. Most grill types are made of cast aluminum and will not rust, but most smokers are steel and once the paint has worn off they will rust (badly). Any rust left on your smoker's surface will keep chewing through the metal, even with a coat of paint on it. Getting down to the base metal will remove this question. You don't have to strip off every bit of paint, just make sure the surface is rust-free, clean, and smooth.
You're ready to paint now. Being careful is the first law of painting something. A few thin coats and not one heavy coat should be prepared for you. Many thin coats are going to be evener, look better, and last longer. Between coats, let the paint dry absolutely. Fire up your grill or smoker to a high temperature once your painting is complete and fully dry. This will fix the paint and make it nice for cigarettes. Over several months or years, repeated paintings will make your grill or smoker even more impervious to rust.
Take good care of your equipment for a very long time and it will support you.