"sudo apt-get install" on OS X Mavericks

If I understand correctly, you just want a package manager.

apt-get is just an interface for Aptitude, a deb packaging system. DEB isn't tied into Mac OS like it would be your average Linux distro, so you'd need an alternative.

Fink will do this on its own, other alternatives are MacPorts or Homebrew.

If your goal is to be able to execute a command, say like (something) install program and it'll install the program and its dependencies for you, either of these three will do that for you.

I'd personally suggest Homebrew. http://brew.sh/

Fink has been released for OS X Mavericks. Per their latest news item…

2013-10-30: fink-0.36.0 released.
fink-0.36.0 was released on 31 October, 2013. This is the first release to work with OS X 10.9 (Mavericks). We are currently in the process of making packages available.

You can download Fink from fink.thetis.ig42.org.