Star One, "Go on a ghost hunt": Go around the castle killing all of the ghosts. Once all of the are killed, a huge ghost will appear in the lobby. Kill him (it takes three hits), and you will receive a star.
Star Two, "Ride Big Boo's Merry-Go-Round": Get into to the basement. This can be done by falling down a variety of holes throughout the level. Go inside the merry-go-round, where you will hear circus-like music playing. Inside, there will be a bunch of little ghosts. Kill all of them, and a large ghost will appear. Kill this too, and you will get a star.
Star Three, "Secret of the Haunted Books": Go into the room with the huge bookshelf. When you go around the bookshelf, there will be three books sticking out on the other end. Hit them in a certain order, and the shelf will lower, revealing a star.
Star Four, "Seek the Eight Red Coins": Collect Eight Red Coins. Most of them are easy, don't forget that there are a few in the coffin room.
Star Five, "Big Boo's Balcony": Get the vanish cap, and go out the door that leads to the library. In one corner of the room, there is a raised platform. Use a wall kick against the right wall (the wall w/o books) to leap up to a hallway above. You now go out the door, and you're upstairs! Once upstairs, go outside, and there will be a Big Boo on a balcony. Kill him, and a star will appear on the roof. You can long jump over to the right side of the roof, then long jump back to the top to get the star. This is a hard one.
Star Six, "Eye to Eye in the Secret Room": Go back to where you got Star #5, and go to the back of the room. You can go through the wall by using the Vanishing Cap. On the other side is a star.
Star Seven: Collect 100 Coins. I really can't guide you through this one.