I would need to install some software (the VC++ 2012 redistributables) on a Windows Azure website. This is part of a troubleshooting procedure related to using ClearScript on a Windows Azure website. More information here: https://clearscript.codeplex.com/workitem/18
Coming back to the question... How can I install the software I need on my dedicated website instance?
If you want to install software on a Azure Web Role then you can do it in 3 different ways as listed here:
If you have an Azure Website (not a role) then you don't have full control of your VM, even if you have a dedicated instance. But there is a way I read that you can possibly install some DLL's, in your project at least, I don't think you will have access to many other folders (or any at all) on your instance.
Windows Azure Website with a Startup task using Webmatrix 3 or similar (without using Visual Studio)