I never leased but have looked into it
With some leases you pay the owner a monthly fee
And you ride on the days that you and the owner agrees to
Some leases the owner pays the board and the farrier and you pay for
Food or the food is included
You can full part or free lease depending on what you want
Personally, I don't like the idea of free leasing. Most people will let you take it to your own barn and the horse is yours to ride and groom, without all of the maintenance expenses. Keep in mind, the owner can take the horse back whenever they want.
Depends where you're at in the world. Where I am from in the US, leasing is common, and easily done. Where I moved to in TX, people looked at me like I had two heads when I asked about leasing. The comment I got, almost verbatim and many times from different people was always "Why would you lease? Just BUY the horse and then sell it when you're done."
It's all in the details though, and those should be spelled out in a lease contract that is mutually agreeable to both parties.
I leased a horse for 5 years and I really liked the set up I had with the owner. Basically she owned the barn and had a horse that needed more of a challenge than just 5 year olds walking him around an arena. I paid $130 per month, and got him 3 days a week. I would show up on my days, saddle him up and ride. I was in charge of making sure he was cooled down right and fed dinner the nights I rode him... other than the leasing fee, I had no other expenses. That for me was the way to go!