data normalization & t-test


this is mp very basic but i just don't get it :confused:

My professor told me:"normalize your data". I read quite some references but all are rather vague... does anybody know a good text (simple :D) that could help me? Or could someone please explain me?

The distribution i am working on is not normal, i have read in various texts that due to this i cannot perform parametric tests like the t-test, ANOVA. While i can perform non-parametric tests, is this correct? are there exceptions?

If i normalize my data, can i do parametric tests or is this irrelevant?