1 Adam: Sightings of the Loch Ness Monster date back to 565, when Saint Columba dealt with a water beast in the River Ness.
2 Jamie: So it wasn't even in the Loch?
2 Adam: It could have swum down the river!
3 Adam: Modern sightings began in 1933 when George Spicer saw a large creature with a long neck crossing the road in front of his car.
4 Jamie: So it wasn't even in the water?? What sort of lake monster is this?
4 Adam: It's a monster! It's not bound by your preconceptions!

Saint Columba, or merely Columba as he was known during his lifetime, was an Irish missionary who spread Christianity through the Scottish highlands region during the 6th century, spending roughly the latter half of his life in Scotland. According to records of his life, he used his clerical powers (not entirely unlike those in Dungeons & Dragons) to banish a ferocious water beast which emerged from the River Ness (which flows from the northern end of Loch Ness).

Wikipedia says:

The earliest report of a monster in the vicinity of Loch Ness appears in the Life of St. Columba by Adomnán, written in the seventh century AD (year 565). According to Adomnán, writing about a century after the events described, Irish monk Saint Columba was staying in the land of the Picts with his companions when he encountered local residents burying a man by the River Ness. They explained that the man was swimming in the river when he was attacked by a "water beast" which mauled him and dragged him underwater. Although they tried to rescue him in a boat, he was dead. Columba sent a follower, Luigne moccu Min, to swim across the river. The beast approached him, but Columba made the sign of the cross and said: "Go no further. Do not touch the man. Go back at once." The creature stopped as if it had been "pulled back with ropes" and fled, and Columba's men and the Picts gave thanks for what they perceived as a miracle.

Modern sightings of a monster near the Loch really only began in 1933, soon after the road along the shore of the Loch was opened to traffic. This began a rash of sightings and something of a public frenzy for the monster, which has only really begun dying off in recent decades as people have found other things to keep them amused, like the Internet and funny cat videos.