They are ripe when they are purple and soft. However I cannot wait till they are ripe enough otherwise the rats with a big tail will get them all(squirrel)

. They steal ALL my fruit so I started disliking them. I take figs off the tree then store in the produce compartment in the fridge. After a few days they become soft and sweeter. If you don't have wild animals around your house then you could let them ripen on the tree.
It's a very good fruit and my mother in law makes fig jam from her own fig trees every year. It's delicious. Fig jam also goes well with some stronger cheese.
If you eat figs as fruit it's better to peel the skin first.