  We develop a practical theoretical formalism for studying the critical
properties of a trapped Bose-Einstein condensate using the projected
Gross-Pitaevskii equation. We show that this approach allows us investigate the
behavior of the correlation length, condensate mode and its number fluctuations
about the critical point. Motivated by recent experiments [Science {\bf 315},
1556 (2007)] we calculate the critical exponent for the correlation length,
observe clear finite-size effects, and develop characteristic length scales to
characterize the finite-size influences. We extend the Binder cumulant to the
trapped system and discuss an experimental method for measuring number
fluctuations.
