What is the ruling concerning a gold ring that my grandmother found on her way and has not used yet?

The ring your grandmother found is considered a "Luqatah" (lost and found item). If it has value, it must be announced for a full year in places where its owner is likely to be found. If the owner does not come forward, she may dispose of it. Then, if the owner appears one day, she should give them the choice either to approve of the charity given, or to take its value.