pacman is Arch Linux's default package manager.

Upgrade the system with pacman -Syu
Remove a package along with unneeded dependencies with pacman -Rsn notepad. Note that this sometimes breaks packages or fails to remove because of intertwining dependencies.

Delete the entire package cache with pacman -Scc. Note that you will not be able to reinstall or downgrade to older packages without a network connection because of this.

Remove unneeded packages with pacman -Qdtq | pacman -Rns -
Keep a package by marking it as explicitly installed with pacman -D --asexplicit package

Remove more packages with pacman -Qqd | pacman -Rsu --print -

Get list of third-party (AUR) packages with pacman -Qqm