When one waveform on a medium meets another waveform traveling across the same medium, we say that the two waves interfere as they pass through each other. It is not quite correct to say that the two waves 'collide' or 'hit'. In classical physics, particles collide and waves interfere.
When two waves interfere, they create a new shape for the medium during the time that they pass through each other. This new shape can obtain a greater amplitude than either wave does separately. This is called constructive interference. For different circumstances, the new wave shape can have a diminished amplitude smaller than either of the amplitudes of the two waves. That is called destructive interference.
Here are several animated wave interference demonstrations:
When periodic circular waves are emitted from two sources, they interfere and form stationary patterns of constructive and destructive interference. The first link here takes you to an interactive animated demonstration of this interference pattern along with a lengthy explanation. The second link sends you to another demo, this one showing these patterns on a surface that is viewed as a 3D animation.
Here are a few videos that present a static three-dimensional representation of several interference patterns: