Each database is different in regards to how its search engine functions, however, there are enough similarties to be able to make some generalizations.
On this page, you'll get pointers for:
The single-box search interface is becoming the most common type of search interface and you'll find it both in web-based databases as well as library research databases. Google and it's subsets (Scholar, Books, Patents), and Library One Search, use the single search box.
Many single-box search interfaces (such as Google and Library One Search) will also provide an "advanced" search screen giving you search boxes for the specific sections (aka "fields") within a record.
The "three row/concept" search interface is the easiest interface to work with when you know not only your concept terms but also their synonyms. This type of interface is an "advanced" search interface most commonly found in traditional library research databases such as ABI/Inform, Compendex, Inspec, and Web of Science.