Most US credit cards use the average daily balance method. Your card agreement or statement will specify which method your issuer applies.
Most US credit card issuers divide the APR by 365 to get the daily rate. Some lenders, particularly certain business and mortgage products, use 360.
If you paid your full statement balance by the due date last cycle, most issuers grant a grace period: new purchases are not charged interest until the next due date. Carrying any balance forfeits the grace period.