One option is to ignore the problem and do ANOVA despite the non-normality. ANOVA is pretty robust with respect to normality violations, so this may be the best option if the non-normality is not too extreme.
A second option is to transform your DV so that it is more normally distributed. If the scores are skewed with a long tail of large values, for example, a square-root or log transform might make the data look pretty normal, so then you could do ANOVA on the transformed scores.
A third option is to replace all scores with their ranks relative to the whole sample, e.g., ranks 1-N where N is the number of scores, and then do ANOVA on the ranks.
With options 2 & 3, you have to think really hard about what an interaction means, since you are distorting the scale of your scores, then averaging, then taking differences of differences. There's no problem if it is a cross-over interaction, but if you are just getting quantitative changes in effect sizes (e.g., factor A effect larger at B1 than at B2), then it may not be clear whether a larger effect in the transformed/ranked scores really reflects a larger effect in the original scores, due to the nonlinear transformation.
