The first one is waiting for you to the left of a the area that wraps and unwraps once you start bouncing on the drums.
You'll need to go hunting a bit for the second one. At a fork in the road with a brown and green bridge, head left over the brown bridge. You'll find it at the top of the hidden squirrel cave. Bounce all the way up to the top to grab it.
The third sits alone wrapped in a flower you'll need to open up, off to the left of the area containing the apples you turn into stalks.
The fourth and final red present is at the top of a tree stump, behind a man and a squirrel taking a break - and, depending on which way you go, is right before or after you nab the jump ability.
The one and only blue present awaits when you help a man who's had his eyes taken from him. Open up the accessories menu, tap on the eye/mouth icon, then pick two of whichever kind of eyes you'd like him to have. He'll be eternally grateful - and give you the blue present.
Your camera helps you bring the world of Tearaway to life, as well as grant you access to create the papercraft in real life, thanks to a nifty web-based uploading system. Whenever you see a pure white object in the world, take its picture to restore it to its full colorful glory.
The first photo is of the King Squirrel, whose crown has lost its color. Take a photo of it to bring it back to its royal hue.
The second photo is of a flower that's lost all its color, right next to one that's in full bloom.
The third photo is of a giant tree that's just to the right of a fork in the road you reach with brown and green bridges. The brown bridge brings you to a Red Present, while the green one lets you move forward.
The fourth photo is of a giant flower that will burst to life as soon as you snap its picture, right before you jump onto a series of tearing drums.
The final photo is of a drum, hiding behind a giant dancing apple near the end of the level. Snap its picture to complete the set of photographs.