One way to make underground paths fairly easily is to build a coaster and use it to bore the tunnel, then after deleting the coaster track, replace it with your path.
When building the coaster use auto tunnel with no more then 9 degrees on the decline. I used somewhere between 8 and 9 degrees. It's nice being able to see the angle displayed as you build, that's new to the last update. [up]
Set the tunnel size to be 18 - 20 feet.
As you continue to build the coaster tracks, bore down to about 25ft and level out before making any turns. Keep your turn angle 30 degrees or less.
If you bring the coaster/ bore back to the surface, remember the incline should be between 8 and 9 degrees max.
Delete the coaster and add your path into the tunnel. You might need to hit the ground outside the entrance with some terrain smoothing to get the path started.
After laying your path, use the terrain tools to shape the entrance as you'd like.
I'm sure auto path tunneling will be added soon. If was spotted in the code during alpha and we could actually switch it on, however it was buggy, for example you could no longer connect paths to rides.