Only have time for a quick reply here, so if I leave something out please don't hesitate to ask. I have tons of experience leasing horses out to others (free off property, paid off property, on site free, and on site paid. So a bit of everything).
Get everything in writing. Like, everything. I'd have to dig out one of my old on site contracts, which I may or may not have on this computer but I can check. If not I am sure someone else here has a good one!
But, essentially, I put everything in. What days do they ride, what tack do they use, are they aloud to change horse's bit without written permission, do they let you know when they are heading off on a trail ride. Put "little" things in too like that horse must be correctly groomed before and after a ride, cooled out property, blanketed accordingly (if you blanket). Put in how long they are aloud to ride for (ex. trail rides are not to exceed 2 hours).
As for money/more official things - you need to put in the contract that payment is due on X date, and no later. If missed payment exceeds X days, you are able to end lease without notice. If they break contract in any way (going on 6+ hour trail rides for example) then you can terminate without notice and no refunds of their money as they broke contract. Generally I put in contract that leaser must give 30 days written notice on the first of the month if they wish to end lease. If it's off property I generally say 60 days notice (case to case depending though). Or, you can do a 6 months/1 years/2 years contract, but say 30 days notice if they wish to terminate sooner.
What to charge? Generally for a trail horse on site lease, you would do a percentage of the board/farrier cost. At only 2 days per week, you should still be responsible for all vet care (unless they obviously cause something to happen), and you are responsible for all miscellaneous things (new blankets, new tack that you wish to have, etc etc). SO, how I calculate lease cost for 2 days per week - lets say your board is $600, and your farrier is $200 every 6 weeks. So $600 divided by average month of 30 days (no refunds for missed days). 600 divide by 30 is 20, so thats $20 per ride, and leaser will ride 8 days in a month (2 per week), so $160 per month would be your lease cost. Do the same for farrier and then you can either just add that in to the monthly lease payment, unless you only have farrier every 2+ months then I'd have that as a separate payment. =)