Troubleshooting application deployed to Windows Azure role is not very comfortable as you don't have your favorite debugging tools there.
Quite easy way how to get them is copying from your local drive when connected to Azure role with Remote Desktop Connection.
Using Azure management tool it is easy to start RDP
but you cannot directly configure sharing of other resources than Clipboard and/or Printer.
To share e.g. local drive C:, save the .rdp link to a file and add following line:
drivestoredirect:s:Local Disk (C:);
Save and open by double-click or Enter. You can now see your local drive in Explorer from Azure.
Update: the same is valid for new portal - by default, the RDP does not contain sharing of local drive.