Almost everything popularly known about druids and oaks rests on a single passage, and it is worth reading rather than repeating.
Pliny the Elder, in Book 16 of the Natural History, describes Gaulish priests holding nothing more sacred than the mistletoe and the tree that bears it, provided it is an oak; says they call the mistletoe by a name meaning all-healing; and describes a ritual on the sixth day of the moon in which a white-robed priest climbs the tree, cuts the mistletoe with a golden sickle, catches it in a white cloth, and two white bulls are sacrificed. Pliny also offers the etymology of druid from the Greek drus, oak, which is linguistically doubtful.
That is the source. It is one paragraph, written in Rome by a man who had not seen it, about a people the Romans were conquering, and it is the only detailed classical account of a druidic rite involving oaks. Julius Caesar in the Gallic War describes druids at some length and does not mention oaks or mistletoe at all.
Ronald Hutton has traced in detail how this paragraph was inflated into the elaborate druidic religion of eighteenth- and nineteenth-century antiquarianism, and how little of that construction has any evidential basis. Golden sickles are archaeologically implausible; gold is too soft to cut with. The oak groves, the white robes and the mistletoe of modern druidry descend from Pliny by way of the Romantic revival, not from an unbroken tradition.
The oak's importance to Iron Age Europe is not in doubt. The specific ritual content usually attached to it is one sentence, heavily embroidered.