Are you wanting to free lease off-site and keep the horse at your property/boarding barn or do you want to on-farm free lease or partial lease?
Looking locally for a lease usually works out better in the long run. Word-of-mouth can go a long long way for leasing, too. There are often families that want to place their horse in a lease situation, but do not want to deal with "tire-kickers" and the strangers that come with online ads.
Call local equine vets, ask if they know of anyone wanting to lease out their horse, and ask them to keep you in mind if they hear of someone. Do the same with local 4-H clubs, boarding barns/lesson barns, farriers, etc.
The more "known" you are the greater the chances of you finding a free lease. If you are not currently taking lessons somewhere, or riding/showing consistently somewhere, and do not have any vet/farrier references, it might be pretty hard to find an off-site free lease, but you may be the perfect person for an on-site partial lease, where the horse stays at the owner's current situation, and you get to ride it a few times a week. You can often find lessons rolled into the partial lease price.
On-site partial leasing a the PERFECT way to get started into horses, without a huge financial cost, and you will generally have a good network to "learn" from wherever the horse is kept.