Here's what I'll do:
You need:
Masking tape & plastic/paper rolls to cover larger areas
Primer aerosol paint (if required, if primer is chipped as well), get the primer that matches the primer on the car.
Correct color matching can of aerosol paint (Autozone, pepboys, etc. would carry most colors. If not, then the dealer)
Clear coat
Prepsol, or similar, to clean areas to be painted. Isopropyl alcohol works, too.
Fine, super fine sand paper
1. Remove any hanging chipped paint.
2. Sand the edges of the chipped areas so the intact paint is perfectly flushed with the primer/bumper. Preferably 1000 grit, I think. After sanding, your fingers should go from the good painted surface, over the damaged area and back onto good paint smoothly with no sharp edge.
3. Mask off everything paint overspray can get on. The only thing that should not be masked off is the painted areas of the bumper (including the damaged area awaiting repair).
4. Wipe the to-be-painted area with Prep-sol or similar to clean off any dust, grime, grease, oil, what have you.
4.5. If you need a primer if the primer peeled off as well, this is the time to do it. Spray the primer over the damaged area. 8"+ away, spray a steady sweeping left to right to left to right from top to bottom in a zig zag line (kinda). You're aiming for a uniformed spray, no excess spraying which can lead to sags. If there is sags, it's not the end of the world.
5. With the aerosol paint, spray the same way as mentioned with the primer.
6. 2 to 3 coats should be sufficient, but wait about 10 minutes between coats, even if the coat doesn't completely cover everything uniformly.
7. When all is dried, wet sand it with a super fine sand paper. This may not be needed if the sprayed paint is uniformed and even.
8. Spray on a layer or two of clear coat.
9. Allow to dry.
10. Buff.
11.
If you happen to have sags, which is paint drips, don't worry! Allow the paint to dry. Once it is dry, use a sanding block which is a foam box with a sand paper exterior. Sand the sags down. The flat surfaces of a sanding block is like a guide when you use it. Once the sag starts to get even with the rest of the surface, you'll know, cuz it'll start sanding the areas around the sag. Then, continue on.
On damages like these, some people do use bondo to fill in the areas where the paint is missing. I don't recommend that, but can be done.
Hope I'm not missing any steps.