You might see the sign "1,000" done with the right hand changing from an "index finger" into an "M" handshape with the fingertips of the index, middle, and ring fingers coming to rest on the palm of the left hand. The Roman numeral for "1,000" is an "M."
I use a version of the sign that has morphed away from the obvious "M" shape and simply uses a "bent hand." You can see how over time the sign would change from using an "M" to simply using a "bent hand."
Here is another view of 1000:
To sign the rest of the thousands, just combine the first part of the number with the bent hand touching the left palm. For example, 2,000 starts with a "2" and then changes into a bent hand and touches the left palm.
See an animated example of the number 2397 (258 KB)
American Sign Language University ™ ASL resources by Lifeprint.com © Dr. William Vicars