What does Sketch do?
Sketch copies the move that the opponent (or ally in double/ triple battles) used last permanently.
For example, say you're battling your Smeargle against Vaporeon, and Vaporeon uses Surf. If Smeargle uses Sketch, then it will learn Surf permanently.
Why do we use Sketch?
Sketch is extremely useful for breeding, as almost any move can be Sketched. Using Sketch, Smeargle can also learn some very powerful moves.
Are there any exceptions to Sketch?
Any move can be Sketched, apart from Chatter, Struggle and Shadow moves.
Moves such as Explosion and Selfdestruct can be Sketched if the Pokemon has Damp Ability.
When does Smeargle learn Sketch?
Smeargle learns Sketch at levels:
1, 11, 21, 31, 41, 51, 61, 71, 81 and 91.