As visual artists, we might rephrase the question as something like: How has the Internet changed the way we see?
For the visual artist, seeing is essential to thought. It organizes information and how we develop thoughts and feelings. It's how we connect.
So how has the Internet changed us visually? The changes are subtle yet profound. They did not start with the computer. The changes began with the camera and other film-based media, and the Internet has had an exponential effect on that change.
The result is a leveling of visual information, whereby it all assumes the same characteristics. One loss is a sense of scale. Another is a loss of differentiation between materials, and the process of making. All visual information "looks" the same, with film/photography being the common denominator.
Art objects contain a dynamism based on scale and physicality that produces a somatic response in the viewer. The powerful visual experience of art locates the viewer very precisely as an integrated self within the artist's vision. With the flattening of visual information and the randomness of size inherent in reproduction, the significance of scale is eroded. Visual information becomes based on image alone. Experience is replaced with facsimile.
As admittedly useful as the Internet is, easy access to images of everything and anything creates a false illusion of knowledge and experience. The world pictured as pictures does not deliver the experience of art seen and experienced physically. It is possible for an art-experienced person to "translate" what is seen online, but the experience is necessarily remote.
As John Berger pointed out, the nature of photography is a memory device that allows us to forget. Perhaps something similar can be said about the Internet. In terms of art, the Internet expands the network of reproduction that replaces the way we "know" something. It replaces experience with facsimile.