brew help will show you the list of commands that are available.
brew list will show you the list of installed packages. You can also append formulae, for example brew list postgres will tell you of files installed by postgres (providing it is indeed installed).
brew search <search term> will list the possible packages that you can install. brew search post will return multiple packages that are available to install that have post in their name.
brew info <package name> will display some basic information about the package in question.
You can also search http://searchbrew.com or https://brewformulas.org (both sites do basically the same thing)