So I wanted to download the blender add-on sapling, but I can't figure out how to download it. I would really appreciate if someone could clarify how to download the add-on.
No need to download the sapling addon, it's already part of blender. Press Ctrl Alt U, go to the Plugins tab, type sapling and enable it.
If for any reason you need to download the addon the link is here: http://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Curve/Sapling_Tree
For other plugin downloads refer to:
One last thing to watch out for is that when you download puffins they are in a text format as .py scripts and not as HTML
Is seems that you accidentaly found a bug report on the addon you want to download. There is no download button. To browse available addons go to the Scripts Catalog. In case of the sapling addon it wouldn't be neccesary (see @cegaton's answer).
On the addon's page you find a download link:
For installation see:
As has been mentioned the addon you mention is included in blender. There are however addons that are in blenders-addons-contrib that people may be interested in downloading and testing. The contrib addons are in development and have not been accepted to be included in stable releases.
There is an overlooked method to access individual addons from blender addons-contrib repository, which can also be used to download updates to official addons after releases.
Start by going to git.blender.org, in the available list select the project you want to look in (blender-addons-contrib.git), at the top of this page click on tree.
Here you can see single file addons have a raw link to the right that you can use to get the file. Items listed as links are folders of more complex addons, if we take one as an example (add_mesh_building_objects) clicking it will show the files that makeup the addon. At the top of the page you will find a snapshot link that will download the folder you are looking at, without downloading the rest of the repository.
You can then unzip this tarball and place it where blender will see it. You may also want to rename it as the folder name will be misleading. The install addon button fails at this point as blender only accepts addons in .py or .zip files and this download will be in tar.gz format. You could unzip and then zip as a .zip file to use the install addon button.