I leased several horses before buying my own. The first few were lesson horses that I leased from the barn, and they charged 1/2 the full care boarding rate (flat rate, no additional fees for farrier or anything like that). These were half leases, and technically I should have had a schedule for which days were "my" days, but these particular horses weren't being used in lessons and didn't have another leasee, so I pretty much got a full lease for the price of a half lease. A nice bonus with leasing the barn's horses was that they were quite flexible about letting me ride a different lesson horse if the need arose or if I just wanted to try out riding a different horse out of curiosity.
The last horse I leased was my "trial run" for buying a horse. It was a full "care" lease from off-site. I found the horse on Craigslist and went to go try out the horse just as if I were buying, then moved him to my barn. There was no fee paid to the owner- I just paid the expenses and took care of scheduling all the normal stuff (full board, vet, farrier, etc.) as if it were my horse. It really gave me (and perhaps more importantly, DH) the confidence that I was ready to buy without the risk of long-term commitment in case it turned out to be more than I could handle.