An easy way to train Smeargle is use it in an in-game double battle, like in the Battle Facility. Use a Pokemon that knows the move and Smeargle. Make Smeargle hold an Iron Ball to slow it down and make sure that the move can be copied. Make your ally use the move, then make Smeargle sketch it. Easy as can be.
Here's a moveset I like to run on Smeargle, just for fun/inspiration.
Smeargle @ Quick Claw
EVs: 252 Speed, 252 HP (4 can be distributed wherever)
Lock-On (or Mind Reader)
OHKO Move (Sheer Cold, Fissure, Guillotine)
This all depends on landing Spore, using Lock-On, and finishing any Pokemon off with an OHKO move. People will hate you if you run this set. But it is oh-so-worth it. If all else fails, use Toxic as a last stand or use Wish before you use Lock-On. Quick Claw is just in case a Pokemon like Deoxys-S is used where you have no chance of outspeeding it.
-Doesn't work against Pokemon with Sturdy
-Doesn't work against Pokemon with Insomnia (If you take Wish)
-Uproar cancels this.