Snap a chalk line a foot away from the wall where you are installing the drainage system.
Remove the concrete from the floor between the chalk line and the wall. You can do this by hand with a pick or use a jackhammer. Clear the chunks of concrete from inside the trench.
Dig out the dirt inside the trench until it's about 12 inches beneath the surface of the floor.
Coat the walls -- including inside the trench -- with a waterproof membrane to seal the walls.
Add a 2-inch layer of gravel into the bottom of the trench, sloping it toward the sump pump hole to improve the drainage. Firm up the gravel base by tamping it.
Attach a PVC elbow to the end of the drain tile that will be on the portion of the trench away from the sump pump.
Protect the drain tile from clogs by wrapping it in landscaping fabric. It won't completely prevent dirt from entering, but it will block most of it.
Lay the drain tile into the trench, with the top end of the PVC elbow extending past the top of the floor. This provides you with access to the drainage system so you can remove any clogs that develop. Keep the top of the elbow covered, during normal operation, to prevent anything from getting into the drainage system.
Add more gravel to the trench until it's flush with the bottom edge of the concrete floor.
Fill the trench with concrete, smoothing the surface with a trowel.