How did astronauts fix Hubble's flawed mirror in orbit?

They fitted it with a pair of spectacles. Hubble launched in 1990 with a main mirror that had been ground incorrectly, resulting in spherical aberration, and a servicing mission in 1993 corrected the optics to their intended quality. Because the mirror was wrong in a precisely known way, the cure could be too.

The mistake was tiny and enormous at the same time. The mirror was smooth to about 10 nanometres, yet its outer edge was too flat by about 2,200 nanometres. That made light from the edge of the mirror focus at a different point from light from the centre, and images of point sources spread over a radius of more than one arcsecond instead of the 0.1 arcsecond the design called for. Nearly all the cosmology programmes became essentially impossible, because they needed to see exceptionally faint objects, and a 1991 comedy even showed Hubble alongside the Titanic and the Hindenburg.

Replacing the mirror in orbit was impossible, and bringing the telescope home would have been too costly. But because the mirror had been ground so precisely to the wrong shape, engineers could design new optics with exactly the same error in the opposite sense, to act as "spectacles". Servicing Mission 1 flew on Endeavour in December 1993 and installed them: COSTAR in place of the High Speed Photometer, and a new camera, WFPC2, with its own correction built in. Charles Pellerin, director of the Astrophysics division, had publicly committed to repairing Hubble by 1994, after redirecting $60 million for the mission.