to answer the drainage area first. if you do not have a downhill area and the water problem is mainly surface water(such as clay soils) then you could use a post hole digger to drill a few holes down about 4 to 5 feet and and put in the drain tile vertically into it and fill around with drain rock or 3/4" crushed rock. this allows surface water to get to subsoil. otherwise drain to a downhill area.
the drain tiles goes into a trench about 10 to 12 inches deep. put in the drain tile(if you can get one with a filter sock on it or use landscape fabric to cover over your rock to keep soil from plugging pipe eventually. trench should have at least a small slope to it to facilatate easy drainage without standing water in the pipe. cover with drain rock or 3/4" crushed rock to about 2 inches from surface and then cover with a good draining soil to plant grass in.
sometimes even just drilling the holes and putting in a vertical pipe and rock will solve some water problems. providing the bottom of the hole is free draining.unless you have lots of deep clay soil.