Using the method of moments to estimate parameters is simply this:
1) Write the parameters in terms of the first few population moments.
2) equate population moments and sample moments
3) solve for the parameters
the result is parameter estimates.
The justification for step 2 of this approach is the law of large numbers.
There's an example of this approach being used on an (untruncated) gamma density here.
So how do you apply it on your problem?
If you can write the moments of the truncated gamma explicitly in terms of the parameters and the known truncation point, you could attempt to solve the equations for the parameters (via methods for solving nonlinear systems of equations).
Failing that, since for a given set of parameter values (and truncation point) you can always find the corresponding moments, you could just quantify the discrepancy between sample and population moments at any given set of parameter values (say via sum of squares of deviations) and use optimization routines (nonlinear least squares should be possible) to minimize the discrepancy (which should go to zero, if that's possible with the specific data for that truncation point, but in any case would be finding a 'best available' in a least-squares-closest-matching-moment sense). The resulting parameter estimates will be method of moments estimators.
(There are functions in the R packages I mentioned in my answer to your other question can evaluate the mean and variance for a given truncation point for many distributions, including the gamma.)