As Scout..

You should stay away from pyro's flame range while being close enough to do damage. You can try ambushing him and try to kill him in 2 meatshots or walk backwards to avoid his flames while being close enough to do damage.

As Soldier..

Shoot your rockets at the floor/walls that are close to the pyro to do splash damage. If the pyro is good at airblasting, use your shotgun to do damage since the pyro needs to change to their secondary/use their flamethrower and try to get close to you. Make sure you have the high ground.

As Pyro..

Try ambushing him with your flamethrower to do damage first. Use your shotgun if you're not in his flame range.

As Demoman..

Don't be close to the pyro since demoman is bad at close combat. Make sure you're out of his flame range. Kill him by getting 2 direct hits at the pyro.

As Heavy..

You can try ambushing since the minigun can shred the pyro up close and the pyro has a lower health than you.

As Engineer..

Stay behind your sentry and use your shotgun at mid range.

As Sniper..

You can easily kill him from long range with your sniper rifle. As long you're faraway and have good aim, you're fine.

As Spy..

You can try backstabbing them. If that fails, don't forget the spy has a revolver.