The intro pic is of the completed project following an overnight storm that dumped at least 3" in a few hours. Typically you'd see a small pond running the distance of the trench with water 2-3" deep and as a couple of feet wide. There was flooding in the streets and low lying areas throughout town, but as you can see the back yard is nearly empty. Here's the rest of the story:
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 rented a trencher capable of digging a 9"x2 1/2" trench for $50 bucks. Sorry, no pics of this, but it was a walk behind (or pull, rather) gas powered unit with a large disk blade. I made two passes of 70' each in opposite directions about a foot apart. This let the machine throw the excess dirt out of the digging area for use later.
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.
Step 2: Fill trench with pea-gravel (quarter minus).
I filled the bottom of the trench with 1-2" of pea gravel. This leveled out the bottom on which I'd place the drainage pipe and would allow better water displacement. Typically you'd probably want to do a good 3" but I wanted to make sure there was room above the pipe for additional dirt/gravel and the sod.