US credit cards issue monthly statements with a due date about 25 days after the date of issuance of the statement. If the monthly statement shows that the full balance due does not include any interest charges for last month, then your account is in good standing and if you pay the full balance shown as due on the monthly statement on or before the due date (doesn't matter if you do it in multiple payments or in one lump sum), then your account will continue to be in good standing and your next monthly statement will not have any interest charges either. What this means is that the purchases that you are making during the current month will show up on your next month's statement but you will not have been charged interest on any of that money that the credit-card company has already paid to the merchants on your behalf. (Note that paying the full amount due, but after the due date, will make your account fall from grace, and you will be charged interest on the following month's statement).
What if the monthly statement balance includes interest charges from last month? Well, your account balance (which may well increase over the month due to new purchases) will accrue more interest which will show up on your next monthly statement. Now, if you pay the statement balance in full by the due date, then you will not be charged interest as of the date of full payment, but your next month's statement will still include the accrued interest on your balance until the date the full payment was received (in timely fashion). So, if you have been carrying a balance on your credit card, it takes two billing cycles to get to the state of nirvana where you are paying no interest at all.
If I make multiple payments on my credit card throughout the month, each time paying the balance in full, will the card company charge interest if there happens to be money on the balance on whichever day they charge interest? Is this strategy good for my credit score?
Assuming that you are paying off the current balance (which includes charges made during the current month) each time, you will not be charged any interest at all, and your monthly statement will generally be whatever amount you charged between the last such payment and the statement date. Generally, this is not a big help in improving your credit scores; in general, the most improvement in scores is believed to occur when the credit utilization is between 5% and 30% of your available credit, and what the scoring agencies see is typically the monthly statement amount as reported by the credit card companies. On the other hand, paying off your balance in full several times a month can help you stretch your available credit if you have a credit card with a low limit (typically offered to students). For example, if your card has a $1500 limit, say, then you might not be able to buy a laptop and a tablet and an airline ticket in one month for that would exceed your credit limit. But by paying off each purchase in full during the month with the purchases spaced a few days apart will work just fine and, with proper planning, might even make you hit the sweet spot of 5-30% utilization of available credit when your statement is issued.