There are many good books on freediving technique, most notably Freedive! by Terry Maas and David Sipperly. Carlos Eyles' Sea Stalking is also a good source. Both books stress gracefulness and relaxation, two things that you'll develop with experience. Don't get overly concerned with bottom time, that will come with relaxation. There's an old saying about fighter pilots that I keep hearing from an old fighter pilot on the freedive-list: "There are old pilots and there are bold pilots, but there are no old bold pilots." The same can be said for freedivers. Take your time and you'll enjoy the sport for the rest of your life.
Practicing deep breathing is a good exercise, both in and out of the water. Take deep breaths and try to fill your lungs from the bottom up. Try and relax your stomach muscles so much that you get a pot-belly from moving your diaphragm down. If you ever get a chance to see Tanya Streeter demonstrate this, its worth a thousand words.
Perhaps the best advice is to get a buddy that's at your same level to dive with. You will both progress at a quick and safe pace, and share the memories of a lifetime. The trust and safety you get from a dive partner is no small thing. If you need more convincing, check out Seth's report on Great White Sharks.
A final word of advice: the swimming pool is no place for practicing your static apnea (breath holds). The number of people that die in swimming pools is alarming, even with trained lifeguards on duty. Practice holding your breath on the sofa or looking at the kitchen clock, definitely not at the bottom of the pool!
Hunting fish under water takes great skill. While a fish is in its own element, you are most certainly not. Even the slowest fish can out swim you, and they will see, hear, or feel you coming long before you can get them in range. It takes a lot of practice before you can lose the clumsiness of a misplaced land animal and acquire the silent grace of a sea creature, and that is exactly what it takes. With the proper technique and equipment you can become more than just an observer of the ocean world. You can become a marine mammal.
As a marine mammal you are not an observer, but an active participant in the circle of life. Knowing this, you have certain obligations: you must take only what you need, you must make every shot count, you must make every attempt to land a fish once shot. This is nothing new. Its the oldest rule in the book.
As a final note, in the ocean big fish eat little fish, and you are not the biggest fish.
Spearfishing doesn't have the wealth of media that other sports do, still, if you dig deep enough you can find some quality materials. The best sources of information are classes, books, videos, web pages, and of course, the divers themselves.
You won't find many beginning classes on freediving. Most dive shops have classes on snorkeling, which may be a good way to start. David Laird teaches a class on "Modern Freediving and Spearfishing Technique", and is probably the best way to start if you are in the San Francisco Bay Area.
There are plenty of good books for beginning spearfishers and freedivers. Some of them are mentioned in our Books section. Check your local library for books on spearfishing and diving. Some of the early works are timeless, while others, though dated, can be very entertaining. (Its interesting to note that those early books almost unanimously state that spearfishing on SCUBA is not sporting. I wonder when that view changed in the USA?) As far as books go, we're all still looking forward to a really good book on coastal spearfishing. Maas and Sipperly, where is it?
There are some videos worth looking at and you can find reviews of them in the Videos section.
The web is full of information (er...you're here, right?) and with a little surfing you'll be up to your ears in information. If you need a starting point try our Links section.
The best resource of all are the divers themselves. "Youth and skill will never overcome old age and treachery," so the saying goes. Find some treacherous old geezer and pick his brain. Mark Barville's Freedive List is like a town meeting hall for geezers, and is consequently the best source of information (and fun) that you are likely to find. The CENCAL Freediver list is also a haven for blue-hairs who are local to Central and Northern California.