If you want to know how well a cheap storm shelter works, just ask any of the 3 little pigs. Only the one made out of brick withstood the 'storm'.
All fun aside, if you're serious about this, cheap is much more likely to get you killed than non-cheap. Depending on what you're trying to protect yourself from, that should dictate to you what you should use in the construction, it's size, and whether it will be above, or below, the ground.
Here's a link. You'll need Adobe Acrobat Reader to read the PDF files but there is quite a bit of choices here. It's Bomb, Blast, and Storm Shelter Plans. If you need more info, e-mail me directly or post up.