There is, indeed, very little information on travelling in that area--on the internet or in guidebooks, in English or Portuguese.
If you look on the internet long enough, you can find some maps (or send me an email address to which to send the ones I have).
The people who helped me the most with my trip were the wonderful Rio guide and all-round good guy Rafael Torres Lopes, whose contact info you can find on this TA site, and a friend of a friend in Sao Luis whose parents live in Santo Amaro. Subsequently, another friend spent about a month in the area, so she may have more info.
The simplest thing to do would be to fly from Fortaleza to Sao Luis and take a bus 4 hours to Barreirinhas.
Sao Luis is an interesting city, with lots of reggae, the historic Reviver district, the lace-making village of Raposa and a boat excursion to the old slave village of Alcantara.
The entry points to the Parque Lencois to see the lakes in the dunes are Barreirinhas and Santo Amaro. Barreirinhas has more tourist infrastructure, but is further from the dunes, so excursions by 4x4 cost more. Santo Amaro is still a little genuine fishing village, right next to the dunes, with a couple of basic pousadas and restaurants.
Atins is reachable by 4x4 froom Barreirinhas.
There is a boat that runs from Parnaiba (Piaui), to the Ilha de Caju, into Tutoia (Maranhao).
When you start travelling off the beaten tourist path in that area (meaning starting from Sao Luis to take an excursion into the Parque from Barreirinhas), you really have to play it by ear, not count on schedules and not be too rigid about getting to a certain place at a certain hour. There is some bus (and 4x4) traffic in the area, but the buses aren't frequent. If you miss a bus or 4x4 connection, you may find yourself waiting hours. Some travel is on sand and is influenced by conditions. (For example, I slept in a supply truck that got stuck in the mud heading out of one village, until the next convoy came through to pull us out.)
No one speaks any English at all, so I would advise learning as much Portuguese as you can and carrying a dictionary and phrase book. If you don't speak good Portuguese (Spanish will not do here), I highly recommend getting to Sao Luis and just taking the bus to Barreirinhas.
I'd be happy to answer any further questions that I can.
Boa viagem.