Valve plans to support the title with microtransactions on virtual items, such as hats. If you paid money for Team Fortress 2, you are automatically a Premium member. Premium members get access to rare and cosmetic items through random item drops, the ability to store more items in their backpack, and more powerful trading and crafting abilities. Gamers who purchase any item with real money from Team Fortress 2's digital storefront will also become Premium account privileges.
Otherwise, the core gameplay is exactly the same for everyone, Premium or free. Valve has posted a FAQ explaining the entire situation - it can be read.