Using the VAO discovery tool is one convenient way to locate datasets you need.

If you need to use Google to locate data, some startups have started using common names for data-related businesses that happen to be the same words formed by observatory/satellite/instrument acronyms (FUSE). Others have acronyms that are the same as more widely-used data products (NED).

Here are some tips to improve your search:

• Add the word "astronomy" to your search, such as ned astronomy data.
• Spell out the full name of the instrument: nasa/ipac extragalactic database data.
• Remove .com results from your query using -site:com: fuse data -site:com

Information about datasets used in a research paper may be included in the bibliography (the best practice), acknowledgments, note, or figure caption. Some researchers are now using institutional or disciplinary repositories for their data.

While NASA ideally has all data in the NASA Open Data Portal, the database is still being populated, and NASA has operated many of its projects for decades. Visit the mission, telescope, and/or ground-based observatory web site to ensure you are not missing any data. 

Do you want documentation (or technical documents) about a specific set of instruments? Google advanced search can be very helpful at getting you where you need. You can use the site: operator to narrow down to a specific subdomain.

For example, a search for documentation site:archive.stsci.edu/fuse will take you to a page about FUSE with links to its documentation. This is admittedly most helpful on larger web sites (such as nasa.gov) with many subpages.

If you want presented data, AstroExplorer is a way to locate astronomy figures, images, and other media in the published literature.