Here is some basic info and concepts you should know.
As said, each distribution maintains an online repository of software, packaged for that particular distribution. It is very very easy to install software available in these repositories. Debian and Ubuntu maintain the largest collection of software of any distro. Most people will find applications to fit all their needs within the repos.
However, if you want software
not available in the repository, it can be more challenging. Probably the most common reason for looking outside the repos is to get a newer version of software than is available. The other reason is for certain closed source or patent encumbered software, usually multimedia codecs.
In many cases there are unofficial repositories people have set up for some of the most popular software not otherwise included in the official repos.
One example is Firefox 3.5. Ubuntu 8.04 ships with Firefox 3.0. If you want the current Firefox, you can add a 3rd party repo to get it.
Ubuntu Blog: Daily Firefox 3.5 / 3.6 Repository For Ubuntu
Another is Pidgin, a multi-protocol instant messaging client. There is a problem with Yahoo messenger that is fixed in a more recent version of Pidgin.
Install or Upgrade to Pidgin 2.6.1 in Ubuntu(Jaunty, Intrepid, Hardy) the easy way | Ubuntu Manual
And lastly, to be able to play commercial DVDs and some other proprietary multimedia, you need to install software available in the
medibuntu repositories.
All of this might seem overwhelming at first, but it doesn't take long to get used to it, and soon it will seem to be a convenient, sensible way to do things. Also less risk of getting malware.