Mathematica automatically loads much of the functionality of the Wolfram Language on opening, unlike other languages which often only provide base functionality until packages are loaded/imported.
For special packages like the one you mention, they can be loaded in at least two ways:
See this page ...
Although, it seems like the question has been addressed in comments, it may be useful to clarify the subject in general. The command Get["http://nrgljubljana.ijs.si/sneg/sneg.m"] does not install the package, it simply loads the package into the Mathematica session from the Web. This does not allow one using it offline.
Installation on Windows
Expanding a comment: we can use GAP to compute large character tables and then import them to Mathematica.
A simple GAP function based on this solution:
storeSymmetricCharacterTable := function(n, filename)
local c, f;
c := CharacterTable("Symmetric", n);
f := OutputTextFile(filename, false);