The first step to navigating research is understanding the Harvard resources available to you.
A useful place to start is http://guides.hcl.harvard.edu/. This website provides disciplinary specific resources for research. A great one to get started on is the Beginner's Guide to Using and Finding Numerical Data.
Emailing discipline specific librarians to find a specific piece of data can also be extremely useful. An overall useful e-mail is email@example.com, which will link you to a data librarian who can help you find what data you need.
In Hollis Classic, you can use the expanded search option to search only for digital materials, and therefore will help you search for data material.
Additionally, the http://eresearch.lib.harvard.edu/V page is a good place to start. You can click on "E-Resources" to search specific resources such as Google Scholar and JStor. Google Scholar is an excellent resources for literature review and bibliographic research. If you are looking for a particular journal, "E-Journals" will allow you to search for specific journals or search journals by discipline. In addition, clicking "Quick Search" and then "Primo Central" will allow you to search specific articles.
Once you are ready to look for data, you can peruse the resources available on this website based on topic. For instance, if you need data on stock prices, you could check the Financial/Business tab. In addition to these links, there are some other resources that may be of interest:
The IQSS Dataverse Network is an excellent resource for accessing virtual data archives.
md4stata provides data sets already formatted for Stata
ICPSR, the inter-university consortium for political and social research provides a large database of social science research
The National Bureau of Economic Research provides a number of varied data sources including macro data, industry data, international trade data, individual data, hospital/provider data, and demographic and vital statistics.
WebLib Polymeta API: Allows you to conduct metasearches across multiple repositories using federated search and results clustering.
Note that if all else fails, a really useful tool is to use a secondary source search, for example search Google Scholar for the subject on which you are looking for data. You will often find another author that has used data you are looking for, and therefore can find the data based on their bibliography.