How do I deal with tipping waitstaff?

I think this is the part that confuses me. She presumably swiped the card the first time. She doesn’t return to the machine a second time with the card. It seems like the tip amount is just written on the slip of paper after the transaction has already finished. Does she then go back to the machine and type that in… without the card? How does that work?

I’ve been eating at restaurants in the US for decades without worrying about that. It just does.

From my vast experience (of sitting in bars and watching because we usually sit down on the end where the horseracing channel is on the TV which happens to be directly above the credit card machine and they hired a new bartender and were traning him while we were sitting there) what happens is that the server goes back to the machine after you’ve added in your tip and pulls up that particular transaction, hits an adjust button, tells the machine how much the tip was, and then hits a submit button and that adds in the tip to that transaction.

I would love to use my bar-sitting/drinking expenses from my taxes due to the educational value derived.