Prepare your paper. Even if you plan on using clear animation cels or celluloid later on, you will start with white paper (or light colored paper if you want a single color background). Printing paper works best, but any thin paper that you can see through without it tearing when you draw will work fine.
Tape the first paper to a light box. If you do not own or have access to a light box, you can use something like a TV or computer monitor, just ensure that your drawing pressure will not crack the screen. The screen should also be a single bright color, preferably white, so that it doesn't disturb your drawing.
Draw your first image. This image is the start of an animation and every other drawing will proceed from this initial drawing. If you are a beginner, focus on the central character or situation in the animation, since creating a detailed background takes a lot of time and practice.
Prepare the next drawing by taping another sheet of paper directly over the first sheet and then drawing a slight variation of that drawing. Do not take your character from standing on two legs to kicking in one drawing, you need to draw each tiny movement as the character moves his leg up and around into a kick. When you finish, remove the first drawing, number it and set it aside. Then use the second drawing to draw the third, the third to draw the fourth and so on, until you have drawn the complete animation. Animation is an extremely detailed and time consuming process so be aware that it may take a long time to finish this step.
Transfer the drawing to a clear animating cel by laying the clear sheet over the paper drawing and tracing over the drawing. You can color the image at this point using markers, paints or whatever tools you prefer. The clear sheet is so that you can use a single background (instead of drawing hundreds of detailed pages) and lay the cels over it one at a time to create your animation. You can scan each image into a computer and then link the files so they are animated or you can film or photograph each cel separately before linking them by hand in the old-school animation style. This is rarely done now, however because it is usually much more labor intensive than using digital tools and software.