Hi,
Bruce Hamilton already explained in detail, I will try to add some extra bits of info.
To distinguish signal from noise level 99% of the time, LOD is taken 3xnoise. Random noise is deemed to follow normal distribution, and noise level is assumed equal to standard deviation. From statistics, we know for normal distributions (gaussian dist. or curve) three standard deviations cover 99% of all distribution.
LOQ or to be more specific LLOQ (low limit of quantification) (since quantification also has some upper limit) leaves some safe area for quantification. It is usually calculated as 2.5 to 3 times LOD or more directly 10 times the noise, but to my knowledge has no physical meaning.
A new approach is using terms such as "decision limit" CCalfa and "detection capability"CCbeta. An international standard, ISO 11843 explains this approach in detail. This incorporates and limits false positives and false negatives but to be fair it's rather complicated, and requires too much statistics knowledge. There are also IUPAC guides for these new "decision limit" and "detection capability", one authored by Lloyd Currie and one from Olivieri (or very similar name).
Very rough summary of the approach: A representative matrice spiked with very low amounts of analyte around the expected limit is analyzed and from calibration curve statistics, standard deviation is calculated and multiplied with some coefficient.
Personally, I wouldn't chose this "decision limit" approach, if it's not obligatory. A EU Commission Directive regarding residues in food and feed, assumed this approach for performance of analytical methods and will be obligatory for EU countries after September 2007 (5 years after directive).
Assuming there are no obligations or guides to follow for your case, I would spike my analytes (or a selected bunch if all at once is complicated) at a very low level (around the expected limit which you can easily find by serial diluting a standard solution) to your matrice for both methods.
Then analyse multiple samples (6-10) from this matrice (each going through sample preparation), and calculate standard deviation for each analyte. Then you may multiply this standard deviation with 3 to obtain LOD and 10 to LOQ.
Best luck,
Bulent