Browse installable applications shows you all the software on these 3 repositories. You can get more by adding more repositories to the list. The good thing about repositories is that when there is a new version of a program, you can upgrade to it automatically using the Application manager instead of periodically checking the developer's website for upgrades. So using repositories should be your #1 choice of install.

If you can't find a repository, look for .install -link. I don't know them that well, but they seem to add the correct repository to your list and install the software.

If you can't find a .install link, look for .deb package. These are like windows installer files. You can open them with application manager or file browser and install the software from them.

When I need some software, I usually just search the ITT forum for it. Pretty much everything is covered here in some form, so it's an easy way to get started. It's good to try to find the official website of the developer or program so you can get the latest version and installation instructions. Some programs have two "latest" versions - the stable and the unstable. Stable is the one that should work well. Unstable is the bleeding edge version with all the new features and bugs.

Many programs depend on others to work, so from time to time you'll probably get error message stating that program can't be installed because some packages are missing. In that case you'll have to check the details of what's missing and install them first. Ideally everything should be in few big repositories so installing and upgrading would be a non issue, but we're not quite there yet