Although installing software on a Macintosh at the root Application level requires admin authentication, many software titles can be installed within a user's account directory without admin authentication.
In order to keep things organized, it's best to install such applications in an Applications folder within your home directory. If it doesn't exit, open a Finder window, select your home directory in the left-hand column, and select New Folder from the file menu. Name this new folder Applications and hit return. The folder will inherit the appropriate folder icon.
There are generally two types of software installers for Mac software: Drag-and-Drop and Package-based installers.
With Drag-and-Drop installers, you can simply open the the software image and drag the application into any local folder. In this case, your personal Applications folder.
As for Package-based installers, you will launch the package and proceed through the installation prompts. When it ask for an installation location, you can specify your personal Applications folder. Be advised that not all Package-based installers will allow you to do this - in those cases, they will generally have to write support files to the system level which always requires admin authentication. If you find you need to install such software, please submit a Support Request, and we will be happy to install it for you.