Spray paint lines where you will install drainage tile. Mark the path of the drainage tile from poor drainage areas to drier areas or established drains or culverts. You do not need to worry about minor yard elevation changes at this point, but avoid moving uphill as you plan your drains.
Dig a trench starting at a point furthest from your drain area. Dig the trench no more than 6 inches wide to prevent crushing the tile later. Check for positive drainage with a string and string level along the length of the trench; keep one-half to one bubble off level.
Line the trench with landscape or filter cloth to prevent roots or silt from clogging the drain. Leave enough extra cloth to overlap the trench near ground level. Install the drainage tile along the length of the trench. Use connectors to add additional lengths as needed. Leave excess tile at the drain area to allow for movement during backfilling; you can cut off excess pipe later.
Backfill the trench with gravel to within one foot of the surface. Add the first few inches of gravel with a shovel to prevent crushing the drain. Use power equipment for the remaining backfill if needed. Use moderate-sized gravel for drainage; do not use granite dust or sand that can clog the drainage system.
Overlap the landscape cloth and cover the gravel-filled trench. Cut off excess cloth and tuck in loose edges.
Fill the remaining trench with topsoil and landscape as desired.