It's rusty already so this isn't easy task and you should consider if you are ready to do this by yourself. Might be easier to disassemble the doors and take them to the paintshop. This might cost you a bit, but you'll be sure it's done properly.
But, if you are ready...
There is a proper way of doing this and a cheap one.
You'll need some paint. Go to the paintshop so they can acquire exact color of your car. Alternatively you might just buy the proper one using color code of your car manufacturer. I don't know Honda, you'll have to investigate. Keep in mind that there is always a slight difference between cars, so the first option is better.
Disassemble doors (so you're left with red-painted element only), sand it properly to the bare metal. Degrease with acetone or any special degreasing fluid, paint with the primer. Let it dry. Then paint them using paint sprayer. Let it dry. Then paint again with the clear coat. Let it dry. Assemble the doors and you are done.
Secure the silver element with paper tape so it won't be painted by accident.
Using sand paper (and probably grinder, as it would be easier), get rid of the rust just in this place. Start with rough like P100, then P400, finish with P800. You have to go down to the bare metal. Don't leavy any rust spots (black points) as the rust will develop from them after time. Degrease with acetone. Next, you'll need to put primer. You might use some kind of active one, that dissolves the rust. They work good, but don't expect any magic here. You have to get rid of the corrosion mechanically first.
After it's dry, you can lightly treat if with sandpaper to smooth the surface.
Then, spray the paint. Do NOT use the brush! It would look very bad. When it dries, put the clear coat and wait until it's dry. Polish it to get even surface.