Both methods start the same way: pay the minimum on every debt, then throw every extra dollar at one target until it is gone, then roll that payment onto the next target. They differ only in how they pick the target.
The avalanche orders debts by interest rate, highest first. It is the mathematically best approach because it eliminates the most expensive debt soonest, which minimizes total interest paid. The snowball orders debts by balance, smallest first. It is the psychologically strongest approach because the first debt disappears fast, and each payoff frees a payment and builds momentum.
Example: a $2,000 card at 26%, a $9,000 card at 19%, and a $15,000 car loan at 6%, with $800 a month available beyond minimums. Avalanche targets the 26% card, then the 19% card, then the car. Snowball targets the $2,000 card, then the $9,000 card, then the car. Here they agree on the first two steps, which is common when small balances are also expensive ones. Where they diverge, the avalanche typically saves a few hundred to a few thousand dollars over the payoff; the snowball typically feels easier to stick with.
Either one beats spreading extra payments evenly across all debts, which is what most people do by default.
The common mistake is spending months choosing a method instead of starting. The best method is the one you will follow for the full payoff. Some people run the snowball for the first one or two small balances and then switch to the avalanche once momentum exists.