Homebrew has dozens of commands, but eight of them carry 95% of daily work. Internalize these and you're fluent.
brew install installs a formula or, with --cask, a GUI app. brew uninstall removes one — and brew autoremove cleans up dependencies that nothing else needs anymore. brew search finds packages by name or regex. brew info shows the package's homepage, version, dependencies, and install path.
brew update fetches new formula definitions from GitHub. brew upgrade installs newer versions of installed packages. The two are commonly chained with brew cleanup to delete old downloaded archives — that three-command dance is the standard weekly maintenance routine.
brew doctor is the first command to run when anything breaks. It diagnoses 80% of common environment problems before you start guessing. brew services manages background processes — it's how you start PostgreSQL, Redis, or any other daemon you installed via Homebrew. brew bundle turns your installed packages into a Brewfile (a text manifest), and lets you reinstall the entire set on another Mac with one command.