Much like aptitude on debian, archlinux also use the same tools to add and remove packages.
pacman is the packages handler on arch, but as on debian there are more then one tool for the job, pacman is the stock like apt-get is on debian. The commands I list here is the minimum you have to know, to handel packages on archlinux. pacman is a command-line tool.
pacman <options> packag1 pack2
to update: pacman -Syu
to install: pacman -S package1
to remove: pacman -R package1
to search: pacman -Ss pack-x
Always good practice to run pacman -Sy before any install, to be sure you get the latest package
Like on debian all the dependencies are solved by pacman.
This is just the most common used, to get the full information on it, go to the archwiki or man pacman.