Pay the highest-interest card first if you want to save the most money. Pay the smallest balance first if you need motivational wins to keep going. The first approach (called the avalanche method) is mathematically optimal. The second (the snowball method) is psychologically optimal for many people who have struggled to stay disciplined.
The avalanche method. List your cards from highest APR to lowest APR. Pay the minimum on every card, then put every extra dollar toward the highest-APR card until it is paid off. Move to the next-highest APR. Repeat until all cards are at zero. This approach minimizes total interest paid because you are eliminating the most expensive debt first.
The snowball method. List your cards from smallest balance to largest balance, regardless of APR. Pay the minimum on every card, then put every extra dollar toward the smallest balance until it is paid off. Move to the next-smallest balance. The wins come faster, which is the entire point: a $400 card paid off in two months is more emotionally satisfying than chipping at a $10,000 card for 18 months.
Concrete example. Imagine three cards: $400 at 18% APR, $3,500 at 24% APR, and $7,000 at 22% APR, with $500 a month available. Avalanche pays the $3,500 card first (highest APR), saving roughly $300 in interest over the full payoff vs. snowball. Snowball pays the $400 card first and gives you a complete payoff in month one. The dollar difference is real but small relative to the total payoff.
How to pick. If you tend to abandon plans when results feel slow, snowball almost always wins because you stay in the plan. If you are coldly analytical and have already proven you can stick to a multi-year plan, avalanche wins. There is no shame in choosing snowball; behavioral economists at the Kellogg School and Harvard Business Review have published research showing snowball users are more likely to actually finish the plan.
Hybrid approach. A common compromise is to use snowball for the first card or two to build momentum, then switch to avalanche for the larger balances. Or keep snowball but make a one-time exception to attack a card with a punishingly high APR (28%+) before going back to smallest-balance order.
What you should not do. Do not split extra payments evenly across all cards. Spreading $200 of extra payment across four cards saves almost no interest and does not give you any motivational wins. Concentration is the entire point of either method.