Valve has confirmed that Dota 2 will indeed be free-to-play, and you'll be able to customize your characters with items from the Dota Store and Steam Workshop.
Now, the game's not released yet. The Store & Workshop introductions are done in preparation for you and the developers. So if you want to play, like right now, then take this Dota 2 survey to enter the pool for a free invitation into the beta if you haven't already.
In the Dota Store you can purchase items to customize your heroes. But, if you're looking for some immediate free alternatives, then look no further and visit the Steam Workshop.
It's important to mention that Valve is not trying to make this a pay-to-win game, so all items are cosmetic and they do not affect gameplay. Also, you can earn any Store item without paying by just playing the game, or trading with other players. There's a FAQ on the Dota 2 website that answers many questions.
Visit the Dota 2 blog for more info, artwork, and videos on the game.