The smart, thorough way of doing it may be (depending on what you are putting in to replace the pasthway with) to dig a shallowish (6-10 inches deep) trench where the path is, laying a couple inches of sand, tamping it (tamp with something crazy heavy, it makes a difference, spud bars with tamps on them work well, but be prepared for a workout, a log of decent density and weight would probably work in a pinch), laying another couple inches of sand, tamping it, hopefully giving you a couple inches thick of tamped sand. Next add some small gravel, tamp lighter than you did sand, add more gravel, tamp again, add dirt, tamp, add dirt, tamp, repeat until the level is right.

However, I'm lazy, so I'd probably just add some dirt, dance around on it until it looked packed in a bit, then add some more dirt and repeat that process, then add grass or whatever.