I believe there are many ways to determine if data is normal or not:
histogram shape
QQ plot
skewness
kurtosis
shapiro test.
Which of the above is the best way to determine if data is normal and one can proceed with parametric tests?
Edit:
After going through this thread (Is normality testing 'essentially useless'?) as suggested in comments by @Luca, I am inclined to conclude that:
Formal tests can be misleading (may show non-normal distribution in large sample sizes, even if data is largely normal); hence can be avoided.
Non-parametric tests should be used for small samples. They are reasonably good even for normal data.
Parametric tests should be for large samples. They are reasonably good even for non-normal large data.
qqnorm(vect) & hist(vect) (R commands) plots may be best for graphic / visual assessment.