Couple of squirts of degreaser. Then soap and water.
Or Swarfega is great.
Or, in a pinch, white spirits. Not terribly good for the skin I expect.
Baby wipes every time.
Brake Cleaner, carb cleaner, WD40.
Swarfega.
Since some smart guys have already said ‘wax’, I’ll go with ‘wear gloves’ as the second smart option 
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Yeah, don’t get the dirt on your hand in the first place. I have a box of disposable vinyl gloves in the garage and keep a pair in my saddle pack for when I’m out on the bike.
I also use a barrier cream or No More Gloves.
That black bike dirt is a microfine (possibly even nanoscale?) powder, its not going to come off whatever you use to wash your hand because it gets within the texture of your skin. Abrasion does work, pumice stone or sand paper but you wont have much skin left.
Baby wipes. They are a tiny bit oily, which is what you want to get the grease off. Works a charm - I use them on the bike as well between wet washes. 4 baby wipes and you can 1) clean chain, 2) jockey wheels (use your nail against that little ridge and turn the pedals to get the built-up grease off), 3) feed the end of one through the front mech and run it back and forth, and then on the chainring teeth, and the last clean one for your hands. Great when away from home especially.
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Baby wipes for cleaning bikes, hands, faces and just about anything!
Dish soap works pretty well but the trick is to use it without water first and wipe off with a paper towel. Sunscreen is ok too, if out and about.