Or maybe you're not understanding how the Ability works...
Every time you win a battle, wild or Trainer (the Pokemon with Pick Up does NOT have to participate), there will be a 10% chance of your Pokemon "Picking Up" an item. It won't tell you it's happened, the item will just appear as a held item on your Pokemon.
It's triggered only by battle, so just walking around with a party full of Linoone won't work, and like Synchronize said, it can't pick anything up if it has a held item attatched already.
If you're battling and it's still not happening, be patient, since it is a 10% chance--you'll get something eventually.
EDIT: No, the level doesn't matter. In Emerald only, what you can FIND with Pick Up is determined by the level of your Pokemon--higher level Pokes pick up better items, but you can still get items with low-level Pokes.