If you repay your payday loan on-time according to the loan terms then the payday loan will not affect your credit score. In most cases it might not show up on your credit report.
If you miss a payment or are unable to pay off the loan, your credit score may be affected and once it taken to collections it will be reported to the major credit bureaus.
Try avoiding late fees with payday loans as bounced checks at a retail store will not appear on tradition credit reports, however if you write a check to a company that reports to the major credit bureau, the late payments could affect your credit score.
Most payday or cash advanced lenders do not report to the major credit reporting agencies unless the loan goes into collections.