How to do "sudo apt-get install " on OSX?
There isn't an equivalent out of the box.
You may want to take a look at MacPorts:
MacPorts, formerly called DarwinPorts, is a package management system that simplifies the installation of software on the Mac OS X and Darwin operating systems. It is a free/open source software project to simplify installation of other free/open source software. Similar in aim and function to Fink and the BSDs' ports collections, DarwinPorts was started in 2002 as part of the OpenDarwin project, with the involvement of a number of Apple Inc. employees including Landon Fuller, Kevin Van Vechten, and Jordan Hubbard.
If you really want an apt-based package management, take a look at Fink. It's the "oldest" package manager on Mac OS X and I'm not sure if the packages are properly maintained anymore. But I'm using it successfully under Snow Leopard.
Others have mentioned MacPorts and Homebrew; it might be worth noting the difference between them.
MacPorts works for me, happily enough. But it has the very annoying feature that it wants to install everything. Thus on several occasions, I've had to drag it back from trying to install its own version of Perl, ignoring the system one, or TeX, and even gcc. Now, the reason for this is, I imagine, that if it were to rely on the system versions of these (or any preinstalled one in the case of TeX), there might be some version-skew issue that would cause something to break. And disk space is cheap. That's probably true, sort of, but it still seems a bit obsessive (and I'm not sure I want to use anything that's quite so dependent on specific versions). Sensible or not, it sets my teeth on edge every time it happens.
Homebrew, in contrast, specifically aims not to duplicate tools that are already installed. When MacPorts does its install-the-world thing, I usually end up killing it and installing the package with the mad dependencies by hand, so I've never quite been driven to the point of using Homebrew, but I've been on the point of doing so, ever since I first heard about it.