What are statistical procedures?

Any of a very large number of tests and comparisons that can be made with data to determine the likelihood that outcomes from various treatments or conditions did not happen by chance alone. The degree to which you can be confident that your results differ from chance is the degree to which you can be confident that the applied treatment is responsible for the results. These treatments or conditions could involve studies of the effectiveness of medications, school performance, biology and physical science research, psychological and social/psychological research... In effect any treatment where you can set up a controlled experiment to obtain measurable results, and where you can compare your results against a properly constructed random model of the same parameters.

Some procedures:

Correlation coefficients

t-tests

Analysis of Variance (with many variations)

Regression

I would broaden this answer. The above definition is limited to inferential statistical procedures, specifically those that endorse a process of null hypothesis significance testing. ANYTHING that deals with data could be considered a statistical procedure (this includes collecting, graphing, describing, and reporting data, in addition to making inferences, testing for effects and estimating effect sizes -- such as the correlation example given above). (Additionally, there are even more variants to regression than there are to ANOVA.) Although the earlier definition properly captures the most traditional aspects of statistical procedures as applied to psychology.