Walking in the desert: walk away from the palace, into the desert at night. About three "steps" away from the palace should be enough.
Wait until the sun rises. I don't remember completely, but I think you'll then get a vision.
It also works in broad daylight, but then you'll loose consciousness, I don't know if there isn't a random factor that perhaps would cause you to die?? So doing it at night might be safer.
To find Stilgar: talk to Harrah (or was it Hannah?). She'll say she remembers a sort of fremen leader, but she's forgotten his name.
Then go talk to the naibs of the 3 sietches you've found early in the game. One of them will tell you the man you're looking for is Stilgar. Then Harrah will remember where to find him. Follow her instructions then.
After you've found Stilgar, you should try to be alone with him (tell Harrah to stay at a certain place, and take Stilgar with you to the next room). Then talk to Stilgar. He'll tell you he wants you to meet someone. This will be Chani. Later on she'll speak about her father (Kynes) and explain where to find him.
Feel free to ask for more hints, I don't want to spoil the game by typing all I remember here. Though there's been a walkthrough circulating on the net, which should be enough to get you through the whole game.
One tip I'd want to add: if you can plant vegetation, don't do it in rich spice areas: plants will destroy the spice. Choose poor areas south of Harkonnes fortresses. The vegetation will grow further north, significantly lowering the Harkonnen's spice mining.
May the spirit of Muad-Dib be with you
