It greatly varies in each situation - be sure that there is a contract to sign with explicit rules for your daughter to follow. I've known some bad situations with owner/leaser conflict that could have been prevented with explicit rules for the lease. They can be super flexible and a great opportunity for kids, but as the adult there are a few things I would specifically be sure to call out in a contract and discuss beforehand.
1. How much work is involved in this situation? Is she only responsible for caring for this horse or will she need to care for other horses too? What does care entail - just cleaning the stall or is feeding involved too? Is it a solely "care for this horse- ride this horse" situation or will she need to log X amount of hours working in the barn to have a "free lease" riding time?
2. How many days is she responsible for the horse? Is this a full lease, 7 days a week she needs to be there or only 2-3 days?
3. In the case of a full lease she may not be responsible for payment for using the horse, but will she be responsible for other financial responsibilities like her farrier or vet bills or feed?
4. Will lessons be required during this lease? Some owners/trainers might require weekly lessons with the horse, in addition to riding on her own. Also ask what she is allowed to do when she rides. For example, if she is jumping in her lessons perhaps the trainer will not want her jumping the horse on her own and having some restrictions.
5. If your daughter is interested in showing - nail down details of whether or not she would be allowed to take the horse to a show or travel off the property.
Those would be the big questions I'd want answered. I'm sure there are more I haven't thought of! Have it all written down in a contract just to protect yourself as well as the trainer. You can never be too thorough!