Cobia can be caught by spinning, plug casting, bottom fishing and by trolling.
Equipment for spinning and plug casting should be a medium to medium heavy rod and reel with 12# to 20# line. Cast lures in front of moving fish so that the lure is reeled across the Cobia’s path. Brightly colored, jigs Bucktail (in white, lime green, yellow) and noisy sinking or diving plugs are popular choices
Equipment for trolling or bottom fishing from boat, bridge or pier would be a medium heavy rod and reel with 20#- to 30# line (Minimum 200yrds.) 2 – 4oz egg sinker on line above swivel, 3’ 40#-50# shock leader with a 4/0 to 7/0 O’Shaughnessy hook. Use live grunts, eels, pinfish, bluerunners or crabs as bait.
Site fishing migrating Cobia is one if the most productive methods for using artificial baits and lures. They are spotted as they travel in shallow water, around pilings, navigational markers, buoys and anchored boats. They will also accompany other large fish and rays. Again remember to cast ahead of the fish so to bring the lure across its path and to work the lure with plenty of action as the Cobia comes near.
Cobia
Rachycentron canadum
Cobia, a.k.a. lemonfish or ling, is an amazing coastal and oceanic species of fish that exhibits what appears to be a regular annual migratory pattern. Current research shows that cobia generally overwinter in the warm waters of the Florida Keys followed by a northward migration to the U. S. north Atlantic and Gulf of Mexico in the spring and summer. Most fishermen feel that the "magic number" in terms of water temperature for ling is 72+oF. Cobia feed primarily on shrimp, crabs, mackerels, and eels and can be found around channel markers, buoys, anchored shrimp boats, and Sargassum weed lines during their migration. These fish probably live to about 10 to 15 years of age, and spawn from late summer to early fall in the southeastern U. S. and Gulf of Mexico. World Record: 135# 9 oz.
http://www.vims.edu/adv/recreation/tag/cobia.html