Tasty little buggers, bluegill are.
I fish for them with a 4'6" ultralight rod, with a tiny little spinning reel and 2 lb. test line. I swim 1/32 oz. jigs, rigged with a flippy little plastic worm about 3/4" long. Sometimes they like the brown ones and sometimes they go for the gold metalflake one. If they won't bite this, substitute small worms for the plastic. Usually, though, swimming that plastic slowly with little twitches on a jig gets 'er done.
No bobbers or any such thing. Keep all the slack out of your line and the little gills just inhale the whole thing. Biggest I've caught was 10" long, and it put up a whale-sized fight on that tiny tackle.
Catch a mess of 'em, then filet them carefully, so as not to waste any meat. Roll 'em in milk, then in seasoned Italian breadcrumbs (they come in a round box), and fry 'em lightly in corn oil 'til they're nice and golden.
Serve the filets with just a squeeze of lemon juice, some nice hot biscuits and a green salad. I can eat more of these than you can count, so I have to catch a big mess of the things if anyone else is there.
Yumm!