Power analysis helps estimate the required sample size for a study. You will need power analysis for experiments, data collection for a survey analysis, etc. The statistical power depends on data types (e.g., dependent data, independent data), the analysis models, etc. It also depends on what you assume about analysis results (e.g., MDES).
For all intensive purposes, "dependent data" means data that are collected from the same subjects at T1 and T2. "Independent data" means the data that came from two groups (control group and treatment group).
One common setup is RCT or QED studies (Randomized Control Trial, Quasi-Experimental Study). Another setup is a survey study where one wants to compare subgroups (e.g., girls vs. boys) or compare t1 and t2 (the same subjects or different subjects).
What Works Clearinghouse considers an effect size of .25 (or greater) "substantively important." See p. 26, table footnote at https://ies.ed.gov/ncee/wwc/Docs/referenceresources/wwc_procedures_v3_0_standards_handbook.pdf
J. Cohen (1988) has an idea of .2 small effect, .5 medium effect, .8 large effect.
Cohen, J. Statistical power for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum (1988). See page 5 of http://www.wmich.edu/evalphd/wp-content/uploads/2010/05/Effect_Size_Substantive_Interpretation_Guidelines.pdf .
Power analysis softwares for RCTs and QEDs:
- Optimal Design https://sites.google.com/site/optimaldesignsoftware/home
- PowerUP http://web.missouri.edu/~dongn/PowerUp.htm
Power analysis for survey analysis (and a lot of other study settings)
- GPower http://www.gpower.hhu.de/