How do you revive a lost language?

There's an interesting article today about the language of the Tunica tribe, who come from Louisiana. This language hasn't been spoken since the 1930s, and a woman called Brenda Lintinger decided to revive it. The question is though, how do you revive a dead language? There are no speakers left, and from the sounds of the article, not much documentation either. There is a 'short grammar' and stories and so on written in the IPA, which would go a long way to understanding it, but surely not enough to learn to speak the language? If you've ever tried learning a language just from a basic grammar, it's pretty tricky. I wonder if there's more available that the article mentions, or if they're only able to get quite basic competence. Still, an admirable effort.