How do I loosen the belt to put back on the car

You will need to loosen the tensioner ?

BELT ADJUSTMENT
Tensioners may be used to automatically adjust belt tension to specification. Check belt for fraying. If fraying exists, ensure belt and tensioner are properly aligned. See Fig. 1 . Tensioners may contain a belt-wear indicator. See Fig. 2 . If tensioner reaches travel limit, as indicated by marks on tensioner, replace belt. Ensure serpentine belts are properly installed. See Fig. 3 -Fig. 5 . On vehicles without tensioners, ensure belt tension is within specification.

Make sure the alternator pulley is the same size as the one which was originally installed. I've had cases where the pulley was larger, which of course meant the belt would not ride up onto the pulley no matter how much I pulled on the tensioner.

The difference is so subtle sometimes, you don't even notice until you're pulling and swearing at the tensioner that it just won't fit.