It's important that you understand exactly what the databases are searching.
Most databases do not actually search and contain the full text of all of the articles. Instead they contain/search metadata.
Metadata is data about the data. It summarizes (and organizes) basic information about the data. Doing this makes finding particular instances of data easier.
Common metadata organizational fields that are searched with a keyword search:
Choosing the right search field can be crucial. You'll get very different results searching "shakespeare" as an author vs. searching it as a subject or within the title field.
Searching purely full-text databases (that is, databases that do not have metadata) successfully can be challenging. This is because you are searching the full-text of everything contained within the database. Full-text searches retrieve huge numbers of results, many of them irrelevant.
You can focus full-text searches by using a "phrase search" (putting quotations marks around words that normally appear side by side) or by focusing your search within a particular field, i.e. title or abstract.