Wash the car, clay inside the handles you'll be working on.
I like to use FG400 by hand on those parts, it gives fast results and I generally only need one 'session' per handle.
Get an applicator (I use LC cyan applicator, or a MF applicator, or a MF towel).
Use plenty of product, not much, but not little. I generally use one or 2 pea size drops.
Spread it on the area.
Use the pressure of one or two fingers on the applicator (or three, or thumb, depending on area you are willing to reach), but try to spread pressure even, not 'very punctual on the tip of your finger' (sorry, it's hard to explain this).
Do movements side to side, with firm pressure (some passion on the pad), and move your hand 'on the speed of light', side to side. Then go up-down, you can even do some circular movements if you can. (again, hard to explain). Then you do movements trying to follow the design of the piece.
Repeat process on the under side (or upper if you started working from bellow).
Wipe off polish residue, and inspect your work.
Generally, some 20-30 seconds of work is enough.
Apply wax, sealant or coating to protect your work.
Points to beware: try to don't exert concentrated pressure while doing this on the edges that 'contour' the handle concavity (!? sorry, try to guess what I'm trying to say). It's not that dangerous by hand, but it's always good to work only on area you pretend to, not hitting anything else 'by accident'.
On the picture you've demonstrated, I'd chose a MF towel to work on your case, you can fold it in 2 then placing your fingers, to give more 'cushion' to apply even pressure and the movement of your fingers.
Hope that helps, please, you can ask if you need more info.
Kind Regards.