In my experience, credit cards in the United States usually have a somewhat generous "grace period" during which no interest is charged.
For simplicity, let's assume that your credit card's billing cycles correspond with calendar months, so that one billing cycle runs from January 1 through January 31, the next runs from February 1 through the last day of February, and so on.
The due date for all of your purchases in January will probably be something like February 25, then the due date for your purchases in February will be something like March 25, and so on. So, if a charge posts to your credit card during the month of February, you won't be charged any interest if you pay that charge off on or before March 25.
If you're concerned about accidentally missing a payment, then I would suggest making a payment once a month, shortly after the end of each billing cycle.
If you want to be even more cautious, then it would be a good idea to pay off each charge shortly after the charge appears as pending. This way, you'll be pretty certain that you're not spending money you don't have, and it's very unlikely you'll ever miss a credit card payment. The disadvantage is that this is less convenient, since you'll be making payments multiple times per month instead of just once per month.
Conversely, if you want to be less cautious, you can schedule payments on the due date instead of before. However, I can't think of any real advantages to this.
Personally, I make credit card payments at an arbitrary time after the end of the billing cycle but before the due date. It doesn't really matter.
What I described above is typical, but different credit cards will have different terms, so the above may not apply to your credit card. Make sure you know how your credit card works before you use it.