As far as books, I highly recommend The Complete Book of Woodworking: http://www.amazon.com/The-Complete-Book-Woodworking-Detailed/dp/1890621366/ref=sr_1_1?ie=UTF8&qid=1335885982&sr=8-1. It's easy to follow even for the uninitiated. It goes over the major tools, what they are used for, and has excellent instructions on some starter and intermediate projects. There are even some workbench projects toward the end, one of which is made only from plywood and 2x4 lumber. I made it with a jigsaw and really uneven cuts, and it's held together well for about a year (it's usable for everything except hand planing). I'm also a software engineer by trade and learn well from books, so I spent a good few months obsessing over this book in my apartment before buying a house and really getting started.
For video instruction, The Wood Whisperer is one of my favorites; he gets into what tools are used for, how to set them up and tune them, and has some videos dedicated to safety. He's also very technical and comes from a science background, so the engineer in me relates well with him. He doesn't leave out many details. Fine Woodworking is also very good and for $5 a month you can get access to a ton of video content.
http://www.thewoodwhisperer.com
http://www.finewoodworking.com
SawmillCreek and WoodworkingTalk are nice forums to search through for tips and discussions about what tools are best used for what projects.
http://www.sawmillcreek.org
http://www.woodworkingtalk.com
Most of these will discuss fine woodworking, furniture making, and detailed joinery, which you may or may not be interested in. All of them, however, will give you information you want about tool usage. It may be more detail than what you're interested in for the projects you describe, but if anything you'll be over-prepared.
Normally a wooden springboard is a laminate of some kind to provide the necessary springyness. It would probably be far easier to buy a board than to make one. If you do want to make one I suggest a design like this (from Popular Mechanics, 1923):
![springboard](https://i.stack.imgur.com/oxl11m.png)
In this design the top plank has a 3-foot overhang, and the middle plank has a 4-foot overhang.
Note that you should use a springy wood such as ash, hemlock, Georgia pine, or hickory. Do not use a random softwood (like a fir) because it is more likely to break.
Note on Diving Boards:
I am assuming you want to build a spring board. A diving board is a rigid board that does not move and is just a platform to jump off. It is actually really hard to make a rigid board that will not warp over time. Oak is a good wood for diving boards because it is strong, tough and rigid.
Best Answer
Board foot is 12x12x1 inches, so 144 cubic inches, so calculate volume in cubic inches (see your geometery teacher/look up online) and divide by 144.
BUT!
If you want to know "how many board feet I need to buy to make (whatever odd shape of whatever volume)" you'll need to go back to rectangular prisms since lumber is sold in rectangular pieces. And even making rectangular pieces, some waste is expected getting from the rough lumber to the finished product.