Depends completely on the owner, the horse, and whatever you work out with them. I did a full lease last year before I bought my horse. It was a free lease - no payments to the owner, but I covered all expenses - board, vet, farrier, feed, hay, and even insurance in case something happened.
My trainer is full leasing a Prix St George schoolmaster and had to pay the owner $1200 for a 6 month lease and all care expenses while she has her.
We also lease several lesson horses at our barn - mostly half leases. Lessee covers half board, feed, and hay, but the barn covers vet and farrier and they usually do 6 month contracts. No limitations on riding. They just coordinate so that riding doesn't occur during lesson times.
"Do the best you can until you know better. Then when you know better, do better."
- Maya Angelou