1. Always lower the pokemon's HP as low as possible, unless if a crit would be too risky.
2. Use a ball that fits the pokemon's design. Heal Balls for girly pokemon, Dive Balls for water pokemon, Nest Ball for grass types, Premier Balls have a burst of red light suitable for fire types, etc.
3. Use the touch pad or analog stick to follow the pokeball's shaking pattern, and tap the screen right when the pokeball clicks.