How did Harry Potter meet the Half-Blood Prince?

Harry Potter didn't meet the Half-Blood Prince directly. He met the owner of the Half-Blood Prince's Potions book, a mysterious and brilliant student from the past, but we never find out who this person actually was.

Here's what happened:

* In Harry's sixth year at Hogwarts, he inherits a potions book from his friend, Ron Weasley. The book belonged to a previous Slytherin student, known only as the Half-Blood Prince.

* The book is full of notes and annotations with clever tricks and insights on potion-making. This helps Harry excel in Potions class, much to the frustration of his rival, Draco Malfoy.

* The book also contains several dark spells and curses. These are what give the Half-Blood Prince his mysterious and somewhat sinister reputation.

* The identity of the Half-Blood Prince is never revealed in the books. Some theories suggest that it was Severus Snape, but this was never officially confirmed by J.K. Rowling.

So, Harry didn't actually meet the Half-Blood Prince, but he did encounter his legacy through the book, which played a significant role in his sixth year at Hogwarts.