This is meant to be a strategy overview for freedivers looking to get the most out of lobster season rather than full, exhaustive tutorial. For information on lobster gear, how to measure a lobster, and Department of Fish and Wildlife license requirements, etc, I recommend visiting the nearest brick and mortar spearing shop or consulting the California DFW website.
When to hunt? Anytime! If hunting during daylight hours you'll want to go to the bottom and look under rocks and ledges, particularly ledges that overhang the sand. At night (or in deeper, dim waters) they may be out on the crawl and you'll be able to spot them with a flashlight, often moving through sand channels or clinging to rocks and other structure. I prefer to hunt lobsters at night--both because there is nothing that can compare to diving kelp forests at night under a full moon, and because it's the most effective use of my time if I'm really targeting bugs.
How to hunt? I like to move fast and cover lots of ground until I find a lobster. The reason for this is two fold. First, they're communal. If I spot one, even a small one, there are likely others very nearby so it pays to slow down and look carefully in the area but move fast until I find that first one. As you do more lobster hunting you'll get better at spotting hidden bugs, with just the tips of their antennae peeking out from under a ledge, and you'll also become better at quickly recognizing the kind of rock piles and ledges that they frequent.
Particularly in the daytime, it is common to spot a lobster in the back of a shallow cave or deep crack but be unable to reach it (per California law, divers MUST grab lobsters by hand. Shooting them with a speargun, using nets or sticks to flush them out is illegal). With experience you learn which is a 'getable' bug and which is not, so when I look in the hole and realize that I can't get the bug, I move on quickly instead of wasting a lot of time trying to coax it out or wiggle myself into a literal tight spot underwater on a breathhold.
Team hunting pays off with bug diving, keep your buddies close for safety and communication--more eyes in the water can mean covering ground more quickly.
Newer bug divers will also quickly learn that to capture a lobster you need to be able to reach its body, tail, or at least the very base of its antennae. If you grab for legs or antennae they will break off in your hand and you'll be left with nothing to show for your effort except the knowledge that you damaged and lost a perfectly good lobster. Lobsters will regenerate their legs and antennae but seeing as they use their antennae to find food, it puts them at a survival disadvantage while new parts grow back.
How deep do I hunt? At night, as a freediver, I typically hunt shallow, maybe 15' to 25'. During the day I may hunt a little deeper, and I've taken them as incidental catch in season while spearing during the day as deep as 90'. I recommend freedivers hunting bugs target areas that are difficult to reach on scuba or by hoop netters (who will be using boats). These will typically be shallower areas. In my experience, if the conditions and terrain is right, I'll be just as likely to find a trophy bug in 3' of water as in 50', although the average size of the bugs I find may trend slightly larger as I get deeper.
Even when hunting shallow, I do not add extra lead to my belt; I am typically finning fast enough that positive bouyancy is not a problem when 'on the swim', and if I find a bug I will grab it on the fly or hold myself into position with one hand and make the grab on the bug with the other. I dive with a small flashlight which is attached by a velcro strap to the underside of my left wrist.
Where to hunt? Terrain which bugs like includes any kind of structure that provides them cover--tight caves, cracks, holes, overhangs, and trenches. This would include wrecks and harbor breakwalls, but if freediving those type of sites, you'll want to take extra care since hook and line fishermen frequent them and there may be an uncommonly high number of human hazards such as ghost hooks and fishing lines around. Secondary terrain which seems to attract bugs include areas with eel grass. Like many of our shallow reef creatures, eel grass is a favorite habitat. In my experience they seem relatively indifferent to the presence of kelp, although any southern California diver knows that the quickest way to find good structure is to find a healthy stand of kelp, so we do tend to head into the kelp forrests when we are targeting lobsters. But, don't overlook urchin barrens if the underlying structure is good. Bugs will also be found in the sargassum, but lobsters don't seem to exhibit any special preference for it. They do seem to like seaweed, so I'll always spend a little extra time on rocks and reef covered with seaweed.
As with hunting any sort of structure, it pays leave a very wide safety margin with bottom times and depths, and practice dropping your lobster bag or weight belt if necessary.
What about the grab, how do I do it? First of all, don't reach into a hole that has a lobster antennae poking out of it until you've checked out what else may be in the hole. Lobsters have very, very poor eyesight--they can see bright lights and will respond if you shine a flashlight directly at them, but they are otherwise nearly blind, so you won't spook any bugs by looking at them. Our southern California reef creatures are relatively benign, but lobsters do share habitat and holes with morray eels (territorial and nasty biters), urchins (sharp spines that break off in your skin), and swell sharks and horn sharks (neither of which are even remotely aggressive, but being large stubborn creatures that breathe underwater I prefer not to stick my hands in their mouths).
During the day, you may find a good crack with several lobsters milling about inside. Often I have caught them by just reaching into the hole and waiting with an outstretched hand until one walked right over my hand. So long as you do not brush their antennae (which are extraordinarily sensitive) they can't see you. At night, I will shine my light around until I've spotted a lobster, then move the brightest portion of my light away and take my time to position myself to grab the bug, keeping it lit in the spill area of my flashlight beam.
Our California Spiny Lobsters do not have pinchers, but their shells are covered with small spikes so you will need to wear gloves when grabbing them.
How do I store live lobsters? The simplest way to store a lobsters once out of the water is to wrap them in a seawater wet towel that has been wrung out firmly, put the bundle in a cooler, lay a frozen water bottle into the cooler and close the lid, and do not disturb them until you are ready to cook or freeze your catch. Kelp also works well in place of a towel; swaddled in damp, cold kelp is their natural intertidal habitat. Ideal temperature is around 55F. If kept this way they'll be fine for at least a day and frequently much longer. Storing them in ice or ice water will kill them, as will submerging them for any length of time in fresh water.
Lobsters, being true intertidals can breathe air so long as they are kept moist and cool, preferably in an environment with 100% humidity. Letting a lobster get too hot or dry out will also kill it. Avoid standing water in the bottom of your cooler since they will drown in even a half inch of water if their mouths are submerged (if wrapping them in a wet towel make sure to wring it out well!) Ice is a bad idea--it's too cold for them and they'll quickly drown in the melt water, and if they don't die their bodies will swell as they absorb fresh water. Some divers get okay results by wrapping them in a wet towel and putting them right in the crisper drawer of a fridge to keep overnight, but mileage will vary with your fridge. Many refrigerators actually have a dehumidifier built in which will dry out their lungs. Putting a caught lobster in an aerated water tank in your home would be illegal under California law.
Lobsters which have lost legs or antennae or who are still soft from having just molted will not last as long and hard shelled whole lobsters, and bigger lobsters last longer than small lobsters. A chilled dead lobster is to be eaten at your own peril; they spoil quickly. A dead room temperature lobster is not even something I would feed to a family pet.
Lastly, if you are interested in some details of California Spiny Lobster reproduction (what exactly does the 'bubble gum' do?), health of our fishery and some ethical questions (is it okay to take 'giant' bugs or should they be left to breed?) here is a great 2017 facebook thread from diver Paul Romanowski, full of fun lobster facts that I've never seen anywhere else: https://www.facebook.com/permalink.php?story_fbid=761552660670406&id=100004470378615&__tn__=C-R