Modernized by Linda Reiff.
R = ring, CH = Chain, RW = reverse work, DNRW = do not reverse work, CLR = Close the ring
SH1, SH2 = Shuttle 1 etc., Floating rings = rings thrown off chains using SH2, + = join
RODS = reverse order double stitch, make the second half stitch first, make the first half stitch second
There is more than one method to tat this pattern. If beginning at the left with the rings on the bottom, try this method.
R 2 ( - 2 ) x 9 clr dnrw rotate the base of the ring 90 degrees to the right.
This direction,( - 2) x 9, indicates that we are to tat a picot followed by 2 double stitches nine times.
Using SH2 (color 2) for the chain, keeping SH1 (color 1) for the core thread, begin chain which goes up and over the ring from left to right. This chain will throw off 3 floating rings and continue on to eventually join to the picot at the mid-point of the first ring.
CH 3 - 4 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 4 - 3 + (join to the middle picot of first ring) 4
Second repeat
R 2 ( - 2 ) x 9 clr dnrw rotate the base of the ring 90 degrees to the right.
CH 3 + (join to picot of previous chain) 4 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 4 - 3 + (join to the middle picot of first ring) 4
Alternate method if beginning with the ring and the chains to be on the right you have the option of tatting the chains in the traditional method, using RODS, or direct tatting (where the ds are wrapped onto the core thread in the manner of a split ring.) 
R 2 ( - 2 ) x 9 clr rw
Consider the RODS method when tatting these chains so that the work will have the all front side up look.
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CH 3 - 4 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 4 - 3 + (join to the middle picot of first ring) 4
CH 4 rw
Second repeat
R 2 ( - 2 ) x 9 clr dnrw rotate the base of the ring 90 degrees to the right.
CH 3 + (join to picot of previous chain) 4 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 3 (using SH2, color 2 R 6 clr dnrw)
CH 4 - 3 + (join to the middle picot of first ring) 4 rw
Original Directions by DMC:
