It's fairly easy to find 'rule of thumb' formulas. Typical of these is this from ARRL: http://www.arrl.org/files/file/Techn...df/9106023.pdf
. It simply comes down to 468 / f (MHz) = dipole length in feet.
To get much more precision, one needs to use such formula as a starting point. As the ARRL article above suggests, you need some means of measuring the actual frequency of resonance once you get close. You'll find that other elements and components near the antenna element will also affect the resonant frequency, not just it's length and diameter.
Now days, it's become common to model an antenna design in software. The number crunching is far faster, and with good software, you get to account for element interactions. 4NEC2 is available for free download, and there's a fair size group of users to draw ideas and experience from. http://home.ict.nl/~arivoors/