Blue sharks are curious and bold creatures. They will work their way up the chum slick and approach the boat. Once sighted, they are prime visual targets for casting tackle, conventional or fly.
When casting live or cut baits with revolving spool tackle, drop the bait several feet in front of the fish's path. It will find the bait soon enough. The same approach applies to flies. Once the fly drops to the surface, let it sink naturally like a piece of chum. In most instances, the angler sees the fish take the offering, pauses for just a second, and then sets the hook. Then it's hang on tight and keep the exiting line clear of obstructions. After the initial run, things will settle down to a good fight.
Some blue sharks do not run far from the boat at all, staying close and dogging down. Others will zip off as if trying to get away. Any heavy shark will have to be pursued with the boat if light tackle is employed.
Rather than chase the fish, lead it. Put the blue shark at the stern quarter, keeping the boat ahead of the fish. While it seems like you are traveling a straight line, the boat is actually making a big circle. In this fashion, by fighting the shark from a side-ways position, the angler can shorten the distance by pumping the fish slowly toward the boat. This technique can be applied to all large fish hooked under most conditions, including sailfish and marlin.