To install drain tile, first make a trench in the ground spanning from the water collection point to an outlet, and insert stakes on both ends of the trench. Determine how much lower the bottom stake needs to be for the system to have a slope, and adjust the trench to fit those requirements. Line the trench with landscaping cloth, and put the pipe in place. Fill the trench with gravel, and top it with soil.
The trench for the pipe should be at least 24 inches deep and 12 inches wide. Connect a string to both stakes, and make sure it is leveled with the bottom of the stake at the higher end of the trench. To calculate how low the bottom end of the trench needs to be, multiply the distance between the two stakes by 0.01. Using the number of inches you've calculated, tie the string to the lower stake to make it lower than its level on the first stake. Adjust the soil to the level of the string; this soil should barely touch the soil at the bottom of the trench.
Using landscaping clothes isn't necessary, but it helps the drain last longer in silty soil. When laying down the pipe, make sure the holes in it are oriented horizontally.