Tipping in the US (at a restaurant)?

Hi,

First of all, I am from Germany, so I am not all that familiar with
the tipping etiquette in the US except for what I have read in a
travel guide and on the Web.

I was in California recently and had a breakfast at my hotel that was
not included in the price for the room. At the end, the waitress
brought me the check in one of those leather envelopes (or whatever it
is called). I only had larger dollar bills at that time, so I couldn't
just leave the amount including the tip on the table. The check had a
line where I could note down the amount of tip, which I did (it was at
least 15 %). She asked "You want me to bring you the change?". I said
yes. She then brought me the exact change without keeping the tip I
noted down on the check. However, I didn't realize that right away and
took all the change. So, now I wonder what I did wrong. Is this line
only looked at when paying with a credit card? Or did the waitress
expect me to take the exact change back and then return to her
personally the tip I wanted to give?

I also saw some people paying to the cashier at the exit. Do you take
your check to the cashier then? I didn't see the people paying to the
cashier leaving any tipping money on the table (doing this may not be
possible if you only have larger bills or a credit card). If/when you
pay to the cashier, how does your waitress get her tip?

One last question: Do you always round up to whole dollars when
tipping even if that would raise the tip a lot?

Regards,
Peter