(abridged) We review methods for measuring the sizes, line widths, and luminosities of giant molecular clouds (GMCs) in molecular-line data cubes with low resolution and sensitivity. We find that moment methods are robust and sensitive -- making full use of both position and intensity information -- and we recommend a standard method to measure the position angle, major and minor axis sizes, line width, and luminosity using moment methods. Without corrections for the effects of beam convolution and sensitivity to GMC properties, the resulting properties may be severely biased. This is particularly true for extragalactic observations, where resolution and sensitivity effects often bias measured values by 40% or more. We correct for finite spatial and spectral resolutions with a simple deconvolution and we correct for sensitivity biases by extrapolating properties of a GMC to those we would expect to measure with perfect sensitivity. The resulting method recovers the properties of a GMC to within 10% over a large range of resolutions and sensitivities, provided the clouds are marginally resolved with a peak signal-to-noise ratio greater than 10. We note that interferometers systematically underestimate cloud properties, particularly the flux from a cloud. The degree of bias depends on the sensitivity of the observations and the (u,v) coverage of the observations. In the Appendix to the paper we present a conservative, new decomposition algorithm for identifying GMCs in molecular-line observations. This algorithm treats the data in physical rather than observational units, does not produce spurious clouds in the presence of noise, and is sensitive to a range of morphologies. As a result, the output of this decomposition should be directly comparable among disparate data sets.
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