This section of tunnel is probably the most accessible section to those new to tunneling. It is easily accessed, there's plenty of room to comfortably walk through most sections, and it runs mostly straight.
The easiest and safest place to access this tunnel is on the Ag Quad in front of Saunders Hall. If you are facing west toward Saunders, you should notice a rusty grate on the ground on the left side of the "Saunders Hall" sign. It should have two parts; lift up the right section first. Be careful when entering the tunnel; there's a ladder located on the side of the grate opposite you. Climb down, making sure to close the grate behind you, and turn to the left. (There's not much to see to the right, but feel free to check it out of you're so inclined.) You are now heading toward Davidson Hall.
On your way, you will pass two grates on your left side. Never use these as an exit; they are on the lower Drillfield and can be easily seen from West Campus Drive and most of the Drillfield.
The tunnel runs mostly straight until you reach Davidson, where it turns to the right and continues on straight toward Burruss. Shortly after Davidson, you will come to a mess of pipes. This is actually where the steam tunnel crosses above the Davidson-Hahn pedestrian tunnel. Continue on, but watch your head while weaseling your way through the pipes; the pipes are padded, but I wouldn't push it. The tunnel continues on straight for a bit; you will pass another grate on your left. Do not use this as an exit either. It's the grate in front of Pamplin and can be easily seen from the Drillfield. Shortly after the grate, you should see some steps. At this point, you will be under Burruss Hall. After the steps, the tunnel will turn to the left.
There will be some steps down, then you will enter a smaller section of tunnel that is very hot. If you continue straight, you will pass a ladder down to the subtunnel that runs toward Hahn North and passes Derring on the way. Be warned, though that the ladder is quite warm, so you will probably want to wear gloves. This subtunnel is very hot, so you won't want to spend long down there. If you continue down the tunnel, you will notice a subtunnel heading toward Derring on your right, behind some pipes. You'll have to squeeze under them if you want to check it out. Although I have not been down this subtunnel myself, I have heard that there is a locked gate down this tunnel which blocks entry into Derring's basement.
After you pass the subtunnel to Derring's basement, you will enter a newer, precast concrete section of tunnel. This leads down toward Hahn North and ends with a much smaller, inaccessible subtunnel where the pipes run into Hahn North. You'll probably have to head back the way you came from here, since there's no way out from Hahn North or Derring.
Back in the main tunnel, if you continue to follow the tunnel toward Cowgill, you will come to another ladder. This ladder is not hot, so climbing down it will not be a problem. The tunnel gets much cooler here and will continue straight until you reach a dead end. Judging by the lack of heat and noise here, I believe these pipes are no longer used. I believe the tunnel used to continue a bit further, but I presume the tunnel was blocked off when Bishop-Favrao was completed in 2007.
If you are ready to get out, I would advise you to follow your path back to the Ag Quad; it's not a good idea to pop out of a random grate or manhole somewhere.