  (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.
