Installing packages and applications works the same way in Mathematica Online as with the desktop Mathematica. Place the package directory into the following location:
Some packages don't follow the standard structure, or require additional setup steps. Read the installation instructions for each package to find out if this is the case.
Mathematica Online only supports packages that are written purely in the Wolfram Language. Anything that has parts written in C or Java won't work. Many Mathematica packages on Hepforge rely on such external components and can't be used with Mathematica Online.
I don't think that it is possible to integrate the documentation into the online documentation browser. Or at least I didn't succeed.
Example with LieART
LieART follows the standard application structure. Its installation instructions tell you to use File -> Install... That method only works with packages that follow conventions.
This package comes as an archive. We have to get the archive into
$UserBaseDirectory/Applications. You can either use the file browser to upload it there (evaluate
UserBaseDirectory to see where you have to browse), or you can download directory with a Mathematica command. I am going to show the latter.
Enter the application directory:
Download the archive:
Check that everything is in place using the file browser on the right, or using the command line:
The package is now ready to use. Load it with
Check what package symbols are available using