The third link in my first reply gives you the best detail of what you need. Find the pictures labeled "Distribution box and large trench details" and Details of leach field trench dimensions and components. They specify 6" of stone below the pipe and 2" of cover, which gives you a total of 12" to 13 " with 4" pipe.
The easiest way to dig the trench is with a bulldozer. For your four pipe system you would need a trench 20 ft wide. A bulldozer will make that quite quickly if you don't have immovable rocks. The downside of that approach is that it will require about 80 cubic yards of stone; probably about 120 tons if they sell it that way. That calculation is based on 13" of stone. Cost of stone is usually a big expense. Try to get prices on crushed stone and on washed and screened natural stone.
If you use the system with separate trenches, and make them only 18 inches wide, you would need only 24 yards of stone. The trenches could be dug with a small backhoe.
Digging trenches 5 ft apart is tricky because the machine may run over into or collapse the adjacent trench. It is also difficult to fill the inside trenches without a bucket loader. That is too much stone for a wheelbarrow. I guess you could fill the outer trenches first and drive over them but it is not a good idea to pack them down too much.
Leach field trenches and pipes are different from sewer drains in that the trench should be almost level. The MAXIMUM slope for the pipes must not exceed 1/4" for every 10 feet. You want the water to stand in the pipes while it drains out or you will lose the effectiveness of the uphill pipes. That is a condition that can usually be achieved only with a surveying type instrument or with very careful leveling with a good level attached to a 10 ft 2x4 and adjusted to be precise. You will not get the backhoe operator to do that and it may require some hand work. You will also have to do a good leveling job with the pipe. The best solution is to put stakes in the ground with an instrument and work from them.
Automatic levels are very easy to use if you can borrow one. I bought one on E Bay for $100 but you also need a tripod and something to use for a level rod. If you can borrow one from a builder or construction friend they will have a tripod and rod.
It would help to know how much of this work you intend to do personally to get some idea about issues of staging machinery. If you hire it done they will come in with a bulldozer and crew and do it all in one day. If you are doing the physical labor you will need to plan on getting equipment to dig the trenches, spread the stone, and backfill with stone and fill after you are done.
If you have access to a small farm tractor with a backhoe and bucket, and are doing it yourself, you could do it one trench at a time. If you have to rent equipment or hire people to come in several times it will probably cost less to hire the whole job done.