After a summer storm my sisters back yard would hold standing water for 2-3 days, meaning that her children and the kids in her daycare would be stuck inside until the lawn was dry enough not to become a sloppy mess. Being the awesome big brother that I am (and because she's letting me temporarily live with her family) I decided to install a drain tile system to make her life easier.
Step 1: Rent a Trencher-Totally worth it
I then would use a trench shovel (flat and narrow) to dig underneith the sod and removed it in 3-4' sections to replace later atop the tiled area. Then, using a spade I dug out the middle of the trench by hand and placed that in a mound that I later removed from the site.