Creating 2-D animations by cutting out paper and creating a flat figure is an easy way to get started with basic animation. The creator's of South Park, for instance, started out using simple construction paper characters. It is wise to use a heavy paper like card stock or construction paper to create your figures.
Try to create each part of the figure separately to ensure the figure can have a wide range of movement. For instance, if your character is a monkey, create a separate head, body, lower arm, upper arm, lower leg, upper leg and tail. You can make the character even simpler by creating only one piece for each arm and one piece for the leg. You can poke a small hole at each joint of your cutout and string them together with dark thread or simply keep them separate. To animate the figures, move each limb slightly and take a picture and then simply repeat the process.
Another great way to create 2-D animation as a beginner is to create a flip book. A flip book is simply a series of pages with drawings on them that, when flipped, create an animation. You can make your own flip book by drawing an illustration on the top page of a sketchbook. Draw a new illustration that is slightly different on the next page. For instance, if you want a flip book of a man running, draw the man standing for the first picture, and then on each subsequent picture, the legs will move up and then down, and the arms will pump forward and backward. You can do a simple test flip book with stick figure drawings to practice.
You can create traditional 2-D animation by drawing and photographing a series of slightly changing pictures. For instance, to animate a man waving his hand, draw several drawings in which the hand is bent, straight, down, back up and bent into the original starting position. Each photograph can be imported into your computer and played in sequential order with a program like iMovie or Movie Magic. Traditionally, old-school animators used film, and each drawing a was a single frame of film.