Set a border around one section of the paper with a pen or pencil, this can be as big or as small as you like. When beginning use a small section, such as a 12-by-3 horizontal grid.
Decide on the dimensions of the pattern for the tessellation. For example, a 12-by-3 grid can be broken into four 3-by-3 boxes laid in a row horizontally.
Create a simple pattern within the grid by drawing down the lines in the paper and drawing variations from the grid. For example, using a 3-by-3 grid, draw down one box and then place a line one box to the left, then down one and back to the right and down to the end. This makes a design where the middle section of the shape shifts one box to the left. Do this for every repetition of the shape. In a 3-by-3 horizontal grid the shift happens every third vertical line. The change must be the exact same for every appearance of the shape.
Refine the shape some more in another area on the page. Choose a different section on the paper, or a different piece of graph paper, and try a more intricate design pattern. Shift lines so that each shape in the pattern interacts with the others. Beginning simply and then becoming more complex is the key to creating a true tessellation. Remember never to allow the shapes to overlap.
Color or fill in each alternating shape to create a checkerboard pattern. See if there are any gaps or overlapping areas within the patter, This makes the tessellation pattern stand out by adding contrast to every other shape.
Create a variety of shapes. The more shapes you have to choose from, the more possibilities you have of finding one that can be progressed into a pleasing tessellation.
Look at each pattern for a slight resemblance of an image. These shapes typically begin as abstracts so use your imagination to find ways in which they can be changed into a specific thing. Like a Rorschach test, look for an image within the shapes. Rotate the patterns to see how they look at each side.
Refine the shape some more to bring out the resemblance to that object. Add interior details to each of the shapes to make that image stand out more. Remember that each repetition must be exactly alike, both inside and outside of the object. If the image only occupies one part of each shape, then shade in the part that is not within the image, but make sure that the shaded area is exactly the same in each occurrence.
Add color to the pattern, adding contrast and visual appeal to the pattern. Tessellations can be black and white or have a variety of colors, but like the pattern itself the colors must repeat exactly.