The Sleeping Forest lies between Bone Village and The Ancient City. If you enter it without the Earth Harp you will run forward but never get anywhere. If you find the Earth Harp in Bone Village the Forest will awaken when you enter.
There is a commonly missed Red Summon Materia, Kjata, on the second screen. Walk to about halfway up the screen and watch the right hand side very carefully. You should see a brief glimpse of red underneath the trees. Quickly run to where you saw it and repeatedly press the Circle button, with any luck you should pick up the Materia. If you miss it and it doesn't re-appear just walk off and then re-enter the screen.
After a few more screens you should leave the forest and enter a rocky area that leads to the Ancient City, there are a few items and chests lurking about, so have a good explore.