Categorical data - how to handle
If the categorical variable is binary(like e.g sex) you try 
Point biserial correlation coefficient.
Or recode levels of var(woman->1, man->0) and use pearson correlation. Recoding it's a risky way because of you indicate order(woman>man). You should be aware of that.

Also $\chi^{2}$ test is used to determine whether an association (or relationship) between 2 categorical variables.

To find association between categorical and numerical variable
try perform One-way ANOVA test.