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The art of capturing Pokémon is no-nonsense that you will need to master. However, there are certain to keep in mind.

• Weaken the Pokémon: Trying to capture a full-health Pokémon shouldn't be attempted. Because you'll miss, and you'll waste a Pokéball in the process. What you'll want to do is weaken it. You can weaken it to 50% to make it vulnerable to capture, but lowering it to as low as 10%-15% is the best. If you miss, try again. If you miss again, weaken the Pokémon more, and try again. You should capture it. If not, you might have encountered a strong-resistance Pokémon, or a rare Pokémon that'll need a stronger type of Pokéball to capture.
• Use the Right Pokéball: The standard Pokéball will capture a vast majority of the Pokémon, as long as you've weakened them enough. For some Pokémon, a stronger ball will be needed, such as a Great Ball or Ultra Ball. Don't waste these stronger Pokéballs, however. Try your regular Pokéballs several times, try weakening the enemy more, and try capturing it again before you waste a more powerful ball.
• Be Patient: If you kill a Pokémon when you're attempting to capture it, don't fret; it happens. With rare exceptions, you'll get the chance to capture that Pokémon again. Just simply run around the area where you originally ran into it, and chances are you'll run into it again. As a last resort, if you can't seem to find that Pokémon again, use the Jhoto/Kanto Map in your Pokédex, or check out the entry for that Pokémon in your Pokédex to find more locations on where you can find that Pokémon, as well as more vital stats and information that might be of assistance in capturing that Pokémon.
• Once Captured, Don't Neglect!: Some Pokémon might not look like much. Some might not even have any attacks. But use that Pokémon in battle (switching it out after the battle starts if you have to, to get it half of the battle's experience) or use an Exp. Share to build it up. Eventually, these weak Pokémon evolve into strong Pokémon.