Many different superposition patterns can emerge when two waves interfere. Lets take a look at a few examples.
In the simulation above, the blue and red waves are traveling in the same direction in the same medium (and therefore have the same speed). The magenta wave on the bottom shows the sum of the blue and red waves. Use the check box to see the red and blue waves superimposed on top of each other. Use the run button in the bottom left corner to turn on the animation.
By default the red and blue waves have the same wavelength and are "in phase". When transverse waves are in phase, they are matched crest-to-crest. The sum of the two waves has twice the amplitude of either of the original waves. This is called constructive interference. Use the slider to change the phase of the blue wave. Watch how their sum gets smaller as the waves get out of phase. When the two waves are completely out of phase, total destructive interference occurs, and the two waves completely cancel.
Now set the two wavelengths to very different values, for example try 0.5 for one and 3.5 for the other. Their sum now shows aspects of each of the individual waves. Adding larger numbers of waves together can create very complex waves sums.