Before you start make sure you have the proper stretchy belt. A standard belt the same size will not work.

I managed to roll off the old one but cutting it off is fine.

If you roll it off you at least have a belt to try the tool required as a trial.

To refit a special tool is required. I bought one but the clearances on the Abarth are too tight to use it. Other models may be OK, so I had to fabricate my own. I made this difficulty 2 because of this. It is really a basic difficulty 1 if you can borrow a tool.

Making tool

You need
24mm ring spanner.
25x15x2mm steel
Welder and grinder.

Fitting the belt

Slip the new belt over the lower pulley
Put the tool through the belt, handle facing forward but above AC pipe. The belt goes on top of the flat steel. Make sure the socket engages the nut on the pulley.
Start the belt onto the front of the pulley making sure the belt stays in the lower pulley (an assistant will help here).
Pull the handle around making sure the belt is feeding onto the pulley.
Pop and it's done.
That was easy wasn't it?(y)