The only way to get Sticks (also known as Leeks) is to take them as held items from wild Farfetch’d. This is the only way to acquire the item in the game, and it’s also only obtainable in the later-game.
You will only encounter wild Farfetch’d after you’ve received the National Pokédex, and only on days when there is a mass outbreak of them. So this is a trickier item to get.
As for what it does:
The Stick is a held item that raises Farfetch’d’s critical hit ratio by two stages, giving each attack a 25% chance of doing double the damage. No other Pokémon in Platinum can use this item.
Getting a Stick from Farfetch’d
Once per day there will be a mass outbreak (also known as a swarm) that randomly causes the encounter rate for a specific Pokémon to spike. These are typically Pokémon that aren’t found elsewhere in the game.
This means you’ll need to obtain the National Pokédex before swarms can start breaking out.
The easiest way to find out which Pokémon is currently swarming is to speak to the little sister of Professor Rowan’s assistant (Lucas or Dawn) in Sandgem Town. Alternatively, you can also watch the Swarm News Flash TV program to find out.
Lucas/Dawn’s house is located directly south of Sandgem Town’s Pokémon Center.
Aside from telling you which Pokémon is swarming, the assistant’s little sister will also give you a Route number to check out.
If Farfetch’d are swarming, head to its habitat area at Route 221 and start searching through the tall grass until you find one.
You won’t be searching for long; a mass outbreak raises the chances of finding a Farfetch’d in the wild from 0% to 40%.
Every Farfetch’d you encounter will have a 5% chance of carrying a Stick, but you can improve the odds and streamline the process by assembling a dedicated item-farming team.
When you find a Stick-equipped Farfetch’d, either catch the Pokémon or use a stealing move like Thief to obtain the item.
Then you can finish the battle however you’d prefer; you’ll keep the Stick even if you flee.
What Does the Stick Do?
The Stick is a held item that boosts a Farfetch’d’s critical-hit ratio by two stages.
Until Farfetch’d’s evolution Sirfetch’d is introduced in Generation VIII, the Stick is about as useless as an item can get.
While a second-stage critical-hit ratio boost would allow you to wreak havoc with a Pokémon, Farfetch’d’s stats are too uniformly low to be of real use in Platinum (with or without stat boosts).
The Stick gives Farfetch’d about a 1-in-4 chance of inflicting 2x damage to its foe. But the Pokémon is unlikely to last long enough in battle to enjoy it—and even then, don’t expect double damage from a Farfetch’d to turn any tides in battle.
So generally this held item is not really worth getting, unless you specifically want to use a Farfetch’d on your team.