Have you thought of which type of analysis you want to conduct? In general, there are three research methods: quantitative, qualitative, and mixed methods. Depends on your discipline, there could be a specific type of data analysis appropriate for your research.
The SAGE Research Methods is a collection of instructional videos and case studies that guide users through the research process. This collection also provide electronic access to the research series for social sciences: Little Green Books for quantitative methods and Little Blue Books for qualitative methods.
Below are direct links to the Sage Research Methods collection:
Data.gov--Provides access to thousands of federal government datasets on various topics. Also allows access to some APIs so you can build an application to access the data.
Inter-university Consortium for Political and Social Research (ICPSR)