The priestess of Apollo sat on a 3-legged stool (tripod). A vase shows Apollo arriving at Delphi on a winged tripod, but the tripod of the Pythia (the name of the oracle of Apollo at Delphi) was more stable.
Some may have believed the intoxicating vapors came from Apollo's slain python. The tripod was said to sit above the python's remains. Hyginus (a 2nd century A.D. mythographer) relates that the python was thought to have delivered oracles on Mt. Parnassos before Apollo killed him.
This photo shows the ruins of the Doric temple of Apollo at Delphi, on the southern slope of the Parnassos Mountain. This version of the temple to Apollo was built in the 4th century B.C., by Corinthian architect Spintharos. Pausanias (X.5) says the earliest temple of Apollo was a bay leaf hut. This is probably an attempt to explain Apollo's association with the laurel. The leaves of the hut came from the bay tree at Tempe where Apollo had gone for his 9-years of purification for the slaughter of the python. Note that there is another explanation for Apollo's association with the laurel, which Ovid describes in his Metamorphoses. In the Metamorphoses, Daphne, a nymph pursued by Apollo begs her father to help her avoid the god's embraces. The nymph's father obliges by turning her into a laurel (bay) tree.
"The Mantic Mechanism at Delphi," by Leicester B. Holland. American Journal of Archaeology, Vol. 37, No. 2 (Apr. - Jun., 1933), pp. 201-214
"The Temple of Apollo at Delphi," by J. Henry Middleton. The Journal of Hellenic Studies, Vol. 9, (1888), pp. 282-322.