I am not familiar with GoDaddy's setup specifically, but in general, you cannot install Django on shared hosting unless it is supported specifically (a la Dreamhost). So unless GoDaddy specifically mentions Django (or possibly mod_wsgi or something) in their documentation, which is unlikely, you can assume it is not supported.
Theoretically you can install Python and run Django from anywhere you have shell access and sufficient permissions, but you won't be able to actually serve your Django site as part of your shared hosting (i.e., on port 80 and responding to your selected hostname) because you don't have access to the webserver configuration.
You will need either a VPS (GoDaddy offers them but it's not their core business; Linode and Rackspace are other options), or a shared host that specifically supports Django (e.g. Dreamhost), or an application host (Heroku or Google App Engine). I recommend Heroku personally, especially if you are not confident in setting up and maintaining your own webserver.
