William first met the Sixth Doctor in a fishing shop, where the Doctor proposed to take William on a fishing trip. William accepted and the Doctor took him to the far future where they entered a fishing competition with a group of future-humans. William travelled with the Doctor in the TARDIS after the competition had ended. (PROSE: Gone Fishing)
Later in his life, as Isaac, he had been undergoing persecution in "his" country and petitioned the ambassador, Nikolai Faro, for asylum in Britain. Faro was intrigued by a piece of music written by Isaac, and had him brought to Britain.
Some time later, Isaac was interviewed by Sarah Jane Smith, with the Third Doctor pretending to be her assistant. The Doctor behaved rudely, and when Sarah scolded him for it, Isaac realised that he was the Doctor, and explained that twenty years ago he had travelled with the Doctor. The Doctor quickly left, aware that Isaac's past was his future.
Sarah visited Isaac for a follow-up interview. He was reluctant to talk, explaining that he knew the rules — he wasn't supposed to discuss the Doctor's future. Before Sarah left, however, he entrusted her with several sheets of music, asking her to keep them safe.
The Eighth Doctor and Flora Millrace travelled back in time and prevented William from joining the Sixth Doctor on the fishing trip, and Flora gave him a recorder instead, telling him to "try something else" other than fishing. (PROSE: DS Al Fine)