Full answer
Browser extensions are the most reliable method. Capital One Shopping (formerly Wikibuy) and Honey (by PayPal) both sit in your browser and automatically pop up with valid coupon codes when you reach a checkout page. Neither requires a credit card.
Retailer newsletters almost always include a welcome discount (typically 10–20%) for new subscribers. Sign up with a secondary email address, grab the code, then unsubscribe if you don't want ongoing email. This works at most mid-sized retailers.
Timing matters: Black Friday and Cyber Monday bring the year's deepest discounts (20–50%), but retailers also run sales at end-of-quarter (March, June, September, December) to hit revenue targets. Carts abandoned for 24 hours frequently trigger a discount email.
For aggregated codes, RetailMeNot and Coupon Cabin are more curated than random Google searches. They show success rate percentages, so you can see which codes were verified recently rather than wasting time on expired ones.