Your hands move forward and back. The tips of the middle finger brush
together as they pass.
There is another common way to sign "internet" but my option is that this
version actually means "network." You touch the middle fingertips
together, then you reposition (change the palm orientation) the hands and
touch the middle fingertips together again. Or you can just keep the
middle fingers touching and wiggle the hands twice.
If you want to express the concept of a "website" what I typically do is I do the
letter W twice, with an arc. This sign is like signing WWW except you
just do "WW" and it seems to fill the role of the concept of the English