The same way you look at any interaction.. See D. C. Montgomery, Design and Analysis of Experiments. D. Booth

This is why I don't like MANOVA as an approach. You are interested in the univariate tests so just run the separate univariate analyses. If you are worried about Type I error control use a general approach like the Holm or Hochberg correction to control familywise error.

MANOVA followed by univariate tests is generally a very inefficient strategy and can dramatically impact statistical power and have poor error control properties. On the plus side it gives a test of a linear function of your DVs that is often near-impossible to interpret and which can't really produce a useful effect size estimate and won't be robust if you try and replicate it with a similar set of predictors and DVs.

There are a few useful applications of MANOVA but I almost never see them in published work.

As was specified above, if your interest is in the individual DVs, rather than a composite optimized for discrimination, do multiple ANOVAs, but correct the hypothesis-wise error rate. But the case is that MANOVA is not only "inefficient" if interest is in individual DVs, it is simply wrong. See the pub below:

Huberty, C. J, & Morris, J. D. (1989). Multivariate analysis versus multiple univariate analyses. Psychological Bulletin, 105, 302-308.