run

RUN: Version 1
This version is a general sign for run that means to "move swiftly on foot so that both feet leave the ground during each stride" (dictionary.com).

Both hands use "L" handshapes. The right index finger is laying up against the left thumb. Both hands move forward as the index finger flex twice. As the index fingers flex, the right index finger wraps around the left thumb. If the thumbs bend a bit that is okay and simply a byproduct of flexing the index fingers.

Animation: "RUN"

RUN: Version 2
Both hands in "L" shapes, palms down. Hands touch at the tips of the thumbs. Hands move forward as the index fingers flex twice.

Animation: "RUN" (version 2)

Note: In English the word "run" can be used to refer to a wide variety of concepts which have nothing to do with using your legs and feet to move swiftly:
a car engine running
run for office
a run in your stocking
a runny nose
"the runs" (diarrhea)
etc.

Each of these concepts would be signed differently and would not use either of the signs for "RUN" (shown above). Instead you would use ASL signs that have closer meanings to the actual concept. For example "run for office" would be shown with the signs "volunteer"-APPLY COMPETE ______" and the specific office being sought (governor, mayor etc.)