On certain places in Braid there will be extremely hidden puzzles for Tim to solve. Each one of them will reveal a star to pick up. In total, there are eight of them. Up in the sky outside Tim's house, there is a constellation showing you which stars you've collected so far. Collecting all eight will reveal the game's true ending.
2-2 The Cloud Bridge
Near the upper right puzzle piece is a slow moving cloud. To reach the star, you have to get on the cloud either by bouncing on the Monstar, or by jumping on the door to jump on the cloud (the latter option requires you to enter the level from the right.) It takes two hours for the cloud to traverse the map. While waiting, read a book, cook a meal while waiting for the cloud to move. If playing on a PC, Alt-tab will not help, as it slows the cloud down by an order of magnitude.
Tim's house
This star requires you to not have put together the puzzle pieces found in World 3 as you need to use them to build the star yourself. When you have collected at least 
Puzzle Piece 3-3-1 and 
Puzzle Piece 3-6-2 as well as either 
Puzzle Piece 2-3-1 or 
Puzzle Piece 2-4-3 you can use these to get your star. Don't worry if you assembled the pieces from World 2, it's only the ones from World 3 that need to be separate.
When at Tim's house, you can see a black rectangle wall acting as a separator between the room leading to World 2 and the one leading to World 3. You can probably see that the wall between these two rooms—unlike the walls between the others—have an opening up top. You need to get into that opening if you want to grab the star here. If you've already gotten the puzzle pieces in 
2-2 The Cloud Bridge, you probably know what to do. Position either Puzzle Piece 2-3-1 or Puzzle Piece 2-4-3 at the bottom right corner of the canvas, get up on its platform, jump up, open the puzzle menu, move the piece a bit up, and repeat until you're all the way up. Stay there for a while, then jump down.
Now go over to the canvas for World 3. If you look very carefully, you might notice a cone in the left window above the canvas, and also a few cracks in the wall immediately below it. Together they kind of look like the beginning to a star shape. Find the two puzzle pieces you need on this canvas and see that they too have shapes resembling parts of a star on them. Try to position these two parts of the star shape at the top left corner of the canvas, so that together with the star shape in the window they form a complete star. This is very fidgety and will probably require many tries. When you hit the sweet spot a sound will play and the star will appear. Rewind time to get back up to the opening you jumped up to before. From here you can simply walk into the star to pick it up.
4-5 Movement by Degrees
To begin with, get back up to the place where 
Puzzle Piece 4-5-2 was located. Find out how to get up there by following the guide for 
4-5 Movement by Degrees. Beyond the three claws, above the monstar cannon is a small platform with the star on it. You need to get past all the claws to get to it, which is rather difficult considering they only ever move when Tim does.
When up on the same platform as the puzzle piece, do like you did when you got up to it. Jump down to below the claws and lead a monstar through the claws to the platform with the puzzle piece on it. You'll have to rewind time to get it past the last claw, just like when getting the puzzle piece. When both Tim and the monstar are on the platform with the piece, bounce off the monstar to get to the platform even higher up; the one making a roof for the puzzle piece.
Up here, do the same procedure again. Jump down and get another monstar through the claw path. When he's pacing the platform with the puzzle piece on it, wait for him to get to the edge of it and jump on him, bouncing over the nearest claw. That's one of the down, just two more to pass.
The next claw is going to be a bit tricky too. Find a position where the second claw is completely down its pipe and wait there for a bit. Then run and try to jump over it. You will not make it and Tim will die. The momentum of Tim's corpse will however still make the claws move. While falling from being dead, you can still control the three claws by rewinding time. Try to keep Tim in a position where the last of the claws you need to pass is down its pipe and let a monstar pass it. Right when he's past, rewind time back to where the second claw was down its pipe and let the monstar pass it to. Quickly jump on the monstar and bounce over the second claw. Two down, one to go.
Just getting past the third claw is no problem, as it's mostly down when Tim pass it, but getting up to the star is trickier. It's too high up for Tim to jump. You will need to go back to where the third claw was all the way down its pipe. Wait for a monstar to pass by it and jump on it, bouncing over the claw. There should be just enough time before you land for another monstar to pop out of the cannon. Land on him to get a large enough boost to take you up to the platform with the star.
