That depends. For some like the Apple credit card they have a simple due date that's the end of every month. For others they often allow you to choose a day of the month as a due date (perhaps aligning with your paycheck date) and is shown on your statement, which gets produced about a month before the due date. And if by the due date you didn't pay off the entire new balance, the interest charges will then appear on the next statement.
Now you can see that for reasonably well off people credits cards offer a nice interest-free float. For example you make a large purchase of $1000 on January 15, but your statement gets produced on February 10 with a due date of March 4. Et voilà you can pay for that $1000 on March 4 with zero interest.