You should not need a GUI installed on the server (just the "skeleton" files installed with the package xserver-common), nor remote desktop, in order to use graphical package management tools. You can instead use ssh -X to connect to the server and run the application:

ssh -c blowfish -C -X username@hostname

You can leave off the -c blowfish and or -C, but if you do, your connection will likely be noticeably slower when running graphical programs. But if you were on a LAN with the machine, then I'd recommend leaving out -C and keeping -c blowfish.

(-c blowfish makes ssh use the blowfish cipher, which is as secure as the 128-bit AES cipher which is otherwise the default, but which tends to be computationally faster, decreasing latency. -C enables compression, if it's available, which increases speed on slow connections--including just about any connection over the Internet--by making it so that there is less data that needs to be transferred. However, -C is not usually helpful on very fast connections such as when the client and server are on the same local area network, because in that case the increased latency caused by performing the computational operations of data compression and decompression can more than cancel out the benefit of transferring a smaller volume of data. See the descriptions of the -c and -C options on the ssh(1) manpage, and Ciphers in the ssh_config(5) manpage, for more details about how to use those flags. And in general, if you are curious about how a command works, you can look at its manual page by issuing the command man command-name or online.)

Then you can install whatever graphical package management utility you want:

sudo apt-get update; sudo apt-get install software-center

Or: sudo apt-get update; sudo apt-get install synaptic

Or: sudo apt-get update; sudo apt-get install update-manager

(You can, of course, install more than one--after running sudo apt-get update, run a command like sudo apt-get install update-manager synaptic.)

Then run whichever utility you want to use, by typing its name (they all have the same executable names as package names...though that is not true for all software in Ubuntu) and pressing enter.

Since you're logged in with ssh -X, programs that you run on the remote server will display their windows and other graphical user interface element on the local (client) machine.

This will likely work out of the box when connecting from another Unix-like system. However, if the client is Windows, then you'll need to use an SSH client that supports X11 forwarding, and you'll need to have an X11 installed and running on the client machine. You can achieve this pretty easily with Cygwin (see the Cygwin/X User's Guide).

It is possible (and quite easy) to install GUI's on an Ubuntu Server system, though it is considered inadvisable to do so for a production system. You can do this yourself (assuming you have administrative rights on the system, and if you don't, then you cannot perform any package management at all!). See the Server GUI documentation. But please take note of the (good) reasons, explained on that page, for why you probably should not do this.