To make a fully-enclosed rabbit run:
1) Obtain some green wire fencing
2) Rent a sod kicker to remove at least a 2' wide section of grass from the yard.
3) Place the sod on a tarp for ease of transfer.
4) Put your wire fencing on the bare dirt, abutting the chain link fence.
5) Cut 5" lengths of wire to attach the green fencing to the chain link fence (at ground level) every foot or so
6) Attach a second length of green fencing to the first, forming the roof.
7) Cut 5" lengths of wire to attach the green fencing to the chain link fence (about 3' up) every foot or so
8) Block off the end of the run by overlapping the wire so it forms a 1/4 circle.
9) Use 5" lengths of wire to secure the end of the run.
10) Cut 5" lengths of aluminum wire to attach the entrance of the run to the cage.
11) Cut an opening to the run through the cage wall.
12) Make a door to separate the run from the cage.
The end of the run in my picture is bare dirt because I ran out of sod. Apparently there were thin spots in my weedy yard. :)