For collecting I usually use a snorkel and go under bridges however if I am looking for things like blue chromis or larger queen angels, I get on a boat and go to one of the sets of coral heads I know about in about 15 feet of water and use scuba. I won't be going over where I go as those spots are natural and I'm concerned may get overfished as it is. A bridge is a man-made structure with a bunch of cement blocks, metal signs, and other marine debris under it. The juvenile recruitment (and ease of catching fish/inverts) is not natural.
Before anything else, you need a dive flag. Many of the bridges are too shallow for motor boats to come screaming through...but they do anyway.
The most valuable tools for collecting are a weighted keep to "keep" animals in and a barrier net. The weighted nets keeps I use are the yellow and weight baitkeepers from Walmart with a 4 lb sandbag dive weight in the bottom of them. The trap door allows me to evert a net with a fish into it. Here is a link.
The barrier nets, I have made myself as I don't think that they are for sale in Florida. It is legal to use monofliament nets for ornamental collecting because this activity is technically tending the net. To make a barrier net you simply cut the center circle out of a cast net, cut one line along the radius to make the net into a long rectangle, and affix bobbers to the non weighted edge. A 6 ft radius cast net will give you a 36+ ft long barrier net (6 x 3.14 X 2 (circumference of a circle)). I like to make another cut and have a 10 ft net and a 25 foot net. For floats I just cut up a pool noodle into 1 inch slices and tie them every few feet with mono-filament to the edge where I cut the middle out. A small hand net, like the green ones you use for fish tanks, is also good for scooping up fish once they hit your barrier net. Small nets are faster but big nets catch bigger fish. I like the green or black aquarium nets that are 5"x7" for things like 2-4" tangs/angels/butterflies and also for strait scooping up lionfish. The 8"x10" aquarium nets are good on their own to setup along a corner and chase fish, like damsels, gobies, and blennies into. They are also good for coralling fragile inverts, such as coral banded shrimp, into. There are some nets called glass nets which are a clear plastic teadrop or square lip around a deep monofilament net. They go for around 50 dollars and are nice for catching things like wrasses, grunts, and big angelfish; fish that try to swim by you instead of away from you on the reef. Here is a link to the place I've bought my glass net. It's the "Large Tear Drop Monofilament Tropical Fish Collecting Net "
I still feel that he barrier net is better for catching big fish (4-12 inches).
A few other things I recommend. Gloves: even gardening gloves work ok but make sure its a tight fit. You can usually find this at the dollar store.
A screw lid Tupperware for small/rare/fragile stuff like neon gobies. These can also be found at a dollar store . Make sure to put many small holes in it and maybe attach a small weight with monofilament so that it doesn't float.
Booties: Fins are more of a nuisance under the bridges for me because you do more grabbing and standing and don't want to kick lots of stuff up.
Rashguard/wetsuit: There are lots of stinging hydroids under there and you definitely don't want a belly of long spine urchin spikes (Diadema sp.).
A lobster bag or mesh laundry bag to keep nets, Tupperware, and maybe a Gopro camera is also good to have.