The skewness and kurtosis of particular distributions are known functions of the distribution. e.g. the Normal distribution has a skewness of 0 and a kurtosis of 3 (often given as an "excess kurtosis" of 0).
The formulas for skewness and kurtosis are widely available on the web, e.g. Skewness and kurtosis
For any given sample, skewness and kurtosis can be calculated by many programs including
PROC UNIVARIATE or even Excel (and doubtless also programs that I am not familiar with, such as
SPSS and so on)
Graphically, tools such as the quantile quantile plot, the density plot and box plots can all be useful in visualizing distributions (including their skewness and kurtosis).