Being a crux user myself, I'll be glad to help you out. Crux is a fairly "barebones" distro, but you'll quickly realise how powerful AND beautiful it is to run, even as a daily driver.

Miatomi's answer was really great, so instead of rewriting it over I'll try to complete it by providing a few correspondances with `pacman` commands, because that's the other package manager i know the most:

seaching packages:
arch: pacman -Ss <keyword>
crux: ports -l | grep <keyword>

building a port:
arch (AUR): cd $PORTDIR && makepkg
crux: cd $PORTDIT && fakeroot pkgmk -d

installing a package:
arch: pacman -U package.tar.xz OR pacman -S <package>
crux: pkgadd package.pkg.tar.gz OR prt-get despinst <package>

(note that the behavior of the second command differ, as pacman will DOWNLOAD and install a package and its deps, whereas prt-get will BUILD and install a packagr and its deps. This is a source based distro after all!)

removing a package:
arch: pacman -R <package>
crux: pkgrm <package>

updating the package tree:
arch: pacman -Su
crux: ports -u

checking packages to be updated
arch: pacman -Qu
crux: ports -d

update everything:
arch: pacman -Su
crux: prt-get sysup

That should be a good starter. Learn how to build and manage packages without `prt-get` at first, to understand the process. But you'll see that it's exactly like what you were used to with the AUR. prt-get being some "yaourt-like" program.

PS: Cédric, is that you? ;)