How does one win free agency?
Perhaps a better question would be, does winning free agency even matter? The Philadelphia Eagles made huge free-agency signings multiple years in a row and created tons of buzz in March and April. Then, when the season began, they fell flat.
The Tampa Bay Buccaneers (after years of underspending) dropped a ton of money in 2012 signing Vincent Jackson, Carl Nicks, Eric Wright and others. Then they only won seven games.
The reason each year's "free-agency winners" don't always do well in the actual games is because there are multiple ways to "do" free agency. Some teams spend all sorts of money just because they have it. Others believe they're one great player from greatness. Still others spend money to help pad the back end of their roster to provide depth in a new scheme or for a new coach.
All of those ways can be successful (perhaps the final two have a higher success rate), so it still comes down to scouting and money management. If a team spends most of its cap space on talented players that fit together, it'll win a bunch of football games. If it spends on overpriced boondoggles or swings and misses on that "last great player," the offseason hype becomes in-season laughter pretty quickly.