Installing themes is no substitute for productive work
... but it sure does provide a nice way to procrastinate.
Since you're using gnome, you can simply double-click the theme package file (the tar.bz or tar.gz) and then look at the readme file. There are different installation methods for different themes, although it is usually as simple as you described-- pointing to the "tarball" (the tar.gz) file and Gnome will unpack and install the theme for you. Once the theme is installed however, you still will need to select it. Some themes however, will have you manually extract the files and copy them to the appropriate folder in your home directory.
Since the theme you're looking at is an "icon theme", you can't just select that "theme". You have to click "theme details" and the the "icons" tab. That particular theme only changes your icons. There are also "controls" themes which chance the controls and "window borders" which change the appearance of the window border and titlebar.
I typically download many themes and piece together a custom theme using the Gnome untility you described.
As for GTK+, it's the graphics library used by Gnome and many of it's applications. The version of GTK+ you *likely* have is 2.6.x or possibly 2.8.x. You should be downloading the 2.6 themes not the 1.2 themes (unless your distro is pretty old and/or hasn't been updated in some time). But sinse you're new to Linux, you've probably got a fresh installation.