Here's an easy to make hologram, one that shows four sides of an object.
It's made by taping together four pieces of plastic to make a truncated pyramid as shown below. On a screen such as a phone, tablet or monitor, display an image or animation that consists of four different views of the same object. Sit the pyramid in the middle and when you look at it from the sides, you'll see the image closest to you projected onto the closest face of the pyramid. And since the pyramid is transparent the image will look like it's suspended in air.
Note that strictly speaking, this isn't actually a hologram. A hologram refers to a thing created using a specific process and involves the "use of laser, interference, diffraction, light intensity recording and suitable illumination of the recording" [from wikipedia]. This pyramid "hologram" is really 4 views using a trick called Pepper's Ghost, the result being something that is popularly known as a hologram.
I've also shown how you can have fun doing Pepper's ghost using a smartphone and a video of some ghosts and an animation of some Star Wars AT-AT Imperial Walkers.
Hologram images to play with
Here are some animations and a still image I've made that you can download and use yourself. Just make your own plastic pyramid and have fun. With some browsers you can just click on the file and you'll be asked to save, with others you may have to right-click and choose to save.
Princess Leia giving here message from Star Wars IV - animation
leia_hologram_h264.avi - 531KB, H.264 video format
leia_hologram.blend - 3.11MB, contains the 3D model and animation for use in Blender, made with Blender 2.71.
Flying pterodactyl - animation
pterodactyl_hologram_h264.avi - 325KB, H.264 video format
Skull - still images
skull_hologram.mp4 - 168KB, video
skull_hologram.jpg - 29KB, still image file
Video - Pyramid Hologram - How to Make/How it Works with Princess Leia Hologram
The following video shows the above hologram in action, including the Princess Leia and R2D2 one, the pterodactyl and the skull, as well as making a plastic pyramid.