How to pay when dining in America

So in New Zealand when you dine at a restaurant you pay at the counter just before you leave. The prices on the menu is what you pay and you do not tip.
I have worked as a waitress in Auckland and when I found money at the table I was clearing up, I was confused; what do I do with these coins?? Tipping is very unusual here but it is customary in America.

Because no one gave me a step by step instruction on what to do after dining in America (which I even Googled while I was still at the restaurant) here it is...

In America after you're done with your meal at a restaurant, the waiter will bring you your bill (or "check", they call it) in a black folder or tray and they will leave. If you have finished your meal and you haven't been given the check, flag down your waiter and ask for it. If you're with other people, usually the check is given to the person who asked for it.
Look at the receipt and you will find an extra amount added on, which is tax. In California where I was, the tax is 9%.
If you're paying by card, put your card in the folder (sticking out so it is visible) and leave the folder on the edge of the table where the waiter will take it.
After they take it, they will bring it back with your card and a receipt to sign.
Sign the receipt and take your card.
If you're paying with cash, put your cash in the folder. They will return with your change.
Multiply the tax amount by 2 (general rule; depends on how good your waiter/ food was) and leave that as cash in the folder on the table.
Or if you're tipping with your card, there will be a blank line on the receipt subtotal for you to write your tip amount. Add it up, write the total you're paying with your card and sign the receipt.
Close the folder and you're done paying! They don't check your signature with your card or anything. This also goes for retail purchases as well. So you can leave as soon as you've signed.

Example:

Meal $20
Tax 9% $1.80
Subtotal $21.80
Tip (18%) $3.60
Total $25.40

You thought your meal was $20? Add tax, add tip... $25.40

This is why I preferred to eat at a foodcourt. You pay upfront and no awkwardness trying to catch the waiter's attention and waiting for them to put your payment through. And you don't have to have cash, because you don't need to tip.
I now know why people say "pick up the check". Cause you literally pick up the check when it arrives at your table!

It may seem so straightforward but I didn't know that they don't check your signature, so I wasn't sure what to do afterwards. Which spurred me to write this... You're welcome!

Signed,

Elisa