How? By grabbing a pilot friend, boarding a light plane, and parachuting down to land on the roof of the Austrian palace containing the jewel.
He then rappelled down a wall and slipped in through a window he had unlocked while on a tour of the palace museum the day before. After disabling the alarm, Blanchard quickly switched out the Star with a replica he had bought in the museum gift shop. It seems it was a very high-quality gift shop, because it took several weeks before anyone noticed the Star was missing. They actually found his abandoned parachute way earlier, but didn't think much of it, because who hasn't suddenly remembered they're wearing a parachute right before entering a museum?
Once he had this historically significant jewel in his possession, Blanchard ... put it in his grandmother's basement and promptly forgot about it. He knew he couldn't fence it; he just took it on a whim, like it was a Twix bar at the supermarket checkout line. He led the cops to it in 2007 after being arrested for some unrelated crimes. Twenty years after this movie-caliber heist, this master thief keeps busy by, uh, getting caught shoplifting gaming consoles at Best Buy. The sequels are always a disappointment, aren't they?