To get a new account with GMX simply follow my link (above) and click on 'Sign Up'. Then just fill in the boxes.
Once you've got a new account, log into it. (Use the same link but click on 'Log in'). Click on 'Mail Collector' and enter your old Outlook (or Hotmail) address and password into the boxes.
Decide if you want copies of your Outlook mail to remain available on the Outlook website (as well as being forwarded to your new GMX address). If so, REMOVE the tick alongside 'Delete e-mails from the third party server after fetching'.
Decide whether you want mail sent to the Outlook address to be kept in a separate folder to anything sent to your GMX address. (It's probably simplest just to have everything arrive in your main Inbox, so REMOVE the tick alongside 'Sort e-mails to a separate folder').
Decide whether you want people (who've sent mail to your old Outlook address) to see your new GMX address when you reply to them. If so, leave the final box unticked. If you'd rather that they still saw your old Outlook address, put a tick in the box.
Click 'Save'.
Thereafter all mail sent to your old Outlook address will automatically be forwarded to your new GMX one, so you DON'T have to advise all your contacts about your new address. They can continue using your old one if they like; you'll still receive all their mail through your new GMX account.
It really is easy!