Are you comparing the means of two groups? If so, you'll probably want a t-test:

Are you comparing the means of two groups between which the observations are independent? If so use a Two-sample independent-samples t-test.
Or are the members of the groups correlated across the groups? For example, perhaps the individuals are the same and were measured two times: before and after a treatment.
If so, use a paired-samples t-test.

Do you just have one group whose mean you are comparing against a known population mean? If so, do you know the standard deviation of that population?

If so, you can use a Z-test. Typically, this is not the case though.
If not, you can use a one-sample t-test. This test accounts for a bit more uncertainty than the Z-test.

Do you just have more than two groups and you want to know if there is a difference in means between any two of the groups? If so, you may want to conduct an ANOVA and conduct an F-test.

Or are your variables categorical and you are comparing the counts of occurances? If so, you'll probably want a Chi-square test.

Do you just have one variable and you are comparing 1) the amount of times you actually observed occurances of various groups against 2) the amount of times you expected occurances of those groups?
If so, you'll want a chi-square "goodness of fit" test.
Or perhaps, you have two categorical variables and you are curious as to whether they are independent based on the distribution of your observations of the occurances in the respective categories.
If so, you'll want a chi-square test of "independence".

Need help deciding what test to use?