Purification is, in my eyes, strictly a matter of containment.
You're usually going to want to tackle most of it BEFORE hardmode starts, but you can still do it after (besides, you tend to have much better pickaxes at that time)
To contain the corruption/crimson/hallow, you just have to make sure there aren't any corruptible materials within 3 blocks of one (crimstone, hallowed grass, corruption's thorns, etc) and to do this, I usually build large vertical shafts all the way to the underworld to box them in. It doesn't HAVE to be to the underworld - but for protecting, say, the Jungle, I usually go all the way.
Use an uncorruptible material, such as Gray Brick or Stone Slabs, as the walls. Make the top a little higher, too, so that thorns can't spread over the barrier.
As for actively purifying? Use the Clentaminator. Burrowing into the afflicted areas and spraying a large area around you is a great way of clearing it up - just make sure you don't miss any single blocks.