you should use the ubuntu package manager as much as you can, this way you'll get updates and only have verified applications installed. The package manager(apt) can be used in different ways. command line using apt-get, aptitude, the synaptic package manager or the ubuntu software center.
If you are using a desktop edition you'll probably want to use the ubuntu software center. If you're working command line you should use either apt-get or aptitude, I'm not really sure what is recommended atm and both work fine.
if you have something that can't be found with these applications it's not in one of the repositories you are using, there are ways of adding a repository, you'll mainly use this if you want a specific set of applications that are maintained by someone else. or you can download the package on the internet, they come in .deb packages as mentioned before.
Once you've downloaded the right .deb package(keep in mind what your architecture is like 32(x86) bits or 64(x64)) and once you've downloaded the .deb you can just double click it and your preferred package manager will start to install the package. If you don't want to use a GUI you can run:
sudo dpkg -i packagename.deb
this will install the package in the same way as described before, only this time command line.
Package management is one of the key issues in the whole architecture, it makes managing installed applications easy and provides a way to use a specific branch type of software like stable and testing for example. Next to that there is the benefit of updates for all your software at once that ubuntu checks on itself.