Are there any methods to determine normality of data and then transform that data to normal distribution if it isn't normal?

The task has been set: It is necessary to conduct research via ANOVA and use Fisher criterion and for this data must have a normal distribution. My question is that if this data contains excess and asymmetry, how can it can be transformed to normal distribution? Even if it possible what are the rigorous methods for determining the normality of distribution? I'm understand that i can watch the histogramm and if this plot looks like a bell curve that this data has normal distribution, but are there more clear ways to designate normality?