Co-ownership:
Watch your terminology - although a lot of us refer to "partners" what you want to build is a co-ownership not a partnership. There's basically 4 ways to own an airplane:
Corporate - create a corporation (the airplane is the asset) and sell shares. This can be very expensive and paperwork hassle but you may have needs for the protection a corporation would give you.
Partnership - create a partnership (watch those tax guys) and have the partnership "own" the airplane. Not recommended.
Co-ownership - As simple as listing the names of the co-owners on the bill of sale and registration. I believe this is limited to either 3 or 4 names. In insurance parlance once you go above 4 co-owners, you are a "club".
Individual - And of course, one person can "own" an airplane.
For a contract, draft a simple contract detailing the co-ownership. There are a lot of sample documents out there or contact a local flying club and see one of theirs. Your biggest headaches are going to be about liquidation or sale of a "share" of the airplane. Make sure the contract states who is responsible for the sale of the share and rights of the other owners for first refusal. For example, you have a 3-way ownership. One owner wants to get out of the group. He has to sell his share. He finds a willing buyer but its a guy who doesn't have a medical and has a reputation of being a little reckless. A common clause is to have a "first refusal", i.e. the other two can refuse the "first" candidate, but the caveat is usually that after the first refusal the others have to either accept the "second" candidate or "buy out" the share. The only other headache that I remember is "weekends". Yes - spell out in advance how many weekends a month each owner is entitled to and how "trades" are made. Believe me, there can be big fights over who gets Memorial, July 4th and Labor Day.
For your books and accounting, divide the airplane costs into two categories: Fixed monthly costs and hourly costs.
Fixed costs will include insurance, tie-down/hangar rental and the regular costs associated with an annual inspection. In one of my old airplanes, it looked like this:
Tie-down: $50.00/mnth
Insurance: $1200/yr or $100/mnth
Annual: $360/yr for fixed inspection ($30/mnth)
i.e $180/mnth split 3 ways was $60/mnth for each "partner".
The hourly costs are gas, oil, maintenance and an engine reserve.
Here's the way you "look" at the picture. The fixed costs are the cost of ownership - if the airplane doesn't fly an hour, you will still have to pay a tie-down, insurance and an annual to keep the bird legal.
Hourly costs are how the owners who "fly" the airplane reimburse the owners who don't fly. You pay for the wear and tear on the parts and for the gas and oil to make it run.
So the first item is gas and oil. Our contract said that the airplane would be left with "full" tanks at the end of every flight unless directed by the next using owner not to do this. Our "log in" sheet had a column where you noted any gas put in the bird because the last guy forgot. On our monthly billing, we had a gas debit/credit line where we would "pay back" the guy who bought the fuel.
Buy oil by the case and save money. Most aircraft burn/blow somewhere about a quart every 3-10 hours. You'll have to determine what your airplane does and then divide by the number of hours.
Maintenance is a sticky one because you have to develop a history. Basically take all your maintenance bills for the year and divide by the number of hours the airplane flew. (A side note here - there are some "maintenance" items that may require an owner assessment to buy a new part. Let's say that you have a Cessna with one of those old Arinc radios and it just gives up the ghost. The shop tells you your choices but everyone is itching for the new Garmin GPS. This is more than maintenance, you are going to substantially increase the value of the airplane.) Back when I was running a club, maintenance was about $13-15/hour for the C-172's and Cherokees. Oh, and I just rolled the cost of oil into the maintenance category.
Finally comes the engine reserve. You buy a plane with 1,000 hours left to TBO. You've got a thousand hours until you hit one great big expense. You can either have a fund ready for this event or you can have a method of telling each member what his/her cost will be when you get to TBO. At a current cost of about $15,000 for an engine overhaul, a normal reserve would be 15K divided by 2000 hours or $7.50/hr.
So for hourly costs, you would show on the bill:
Gas Debits/Credits: 16gals @ $2.50/gal = $40.00 (to B. Smith)
Maintenance: 14.50 hours @ $12.00/hr = $174.00
Engine Rserv: 14.50 hours @ $7.50/hr = $108.75
In this scenario, our "owner" flew his airplane 14.5 hours in the logbook. His costs were $60.00 fixed and $283 for hourly not including fuel. If you took a typical C-172 and $2.50/gal for fuel: 14.5 times 8gph times $2.50/gal = $290. Our hero flew 14.50 hours for $633 or $43.65/hr.
Good luck on setting up your plane!
Get a copy of the booklet "Plane Sense" from the FSDO (AC 20-5G). It explains a lot of the paperwork in buying a plane.