See also Arch Pacman Reference
pacman -S <package> # Install <package>
pacman -R <package> # Remove <package>
pacman -Rn <package> # Purge <package>
pacman -Rs <package> # Remove including orphaned dependencies
pacman -Qdt # List all orphaned packages
pacman -Sc # Clean package cache
pacman -Syu # Update all packages
pacman -Ss <package regex> # Search for <package regex>
pacman -Si <package> # Detailed info on <package>
pacman -Qs <string> # Search for installed packages
pacman -F <string> # Search for files in packages
pacman -Ql <package> # List all files installed by <package>
pacman -Qo <filename> # Check which package installed <filename>