DISCLAIMER: I'm NOT the dev.
Nonetheless, I think I figured out what the first couple points in each thing does.
The first skill 'Tip Windows Increase' increases the patience of each customer in terms of how long they will wait to be served before they stop tipping.
More points here means you can take longer to serve a customer and still get a tip.
The second skill 'Get Drink Action' increases the number of drinks you can load at once from 1->2->3.
Not sure of whether or not there is value beyond the second level since I don't think the tray can hold more than 3 drinks at once anyhow.
The third skill 'Number of Action' is the least clear of the bunch to me.
AFAIK, the effect of investing in this skill is that you can just do more stuff (generally speaking) before the timer ticks another 0:15 increment. Effectively, it seems to allow you to pack more action into any given day.
With that understanding, I personally went for my first skill point into Tip Windows Increase, then the next into Get Drink Action, then into Number of Action, again into Tip Windows Increase & Get Drink Action, and then any further points will probably be invested into Number of Action from that point on unless somehow you can actually put more than 3 drinks on the tray or patrons stop being willing to tip with only 2 points invested.
TLDR: I don't think the skill system is really far enough along to worry too much about what it does, but here's some info (from a random dude!) if you're curious.