ENCOUNTER
Where wild Pokémon are listed, roll the Capture Dice to initiate an encounter. Every Pokémon is listed at a certain rarity level. Roll a certain number, and you will encounter a Pokémon under that rarity level. You can decide the exact species.
Roll 1-18: Very Common encounter
Roll 19-32: Common encounter
Roll 33-40: Uncommon encounter
Roll 41-45: Rare encounter
Roll 46-50: Very Rare encounter
If you roll a number but a Pokémon isn't listed under that rarity level (e.g. there are no Very Common Pokémon), then you run into nothing.
Sprites represent an entire evolutionary chain. For example, in an area with wild Bulbasaur listed, that means there are also wild Ivysaur and Venusaur. However, stick with encounters appropriate for your tier. You can't have a First Tier Charizard.
CAPTURING
Once you encounter a wild Pokémon, you will be able to attempt to attempt a capture if you wish. Trainers have three options: Battle, Capture, or Run. Running will end the encounter. Capturing will use up one of your Poké Balls in a catch attempt. Battling will whittle down the wild Pokémon's health and make it easier to capture, but has a chance of scaring the Pokémon off and causing it to flee.
Choose Battle 0 times, Roll Dice: 1-5 capture, 6-50 break free
Choose Battle 1 time, Roll Dice: 1-5 KO, 6-20 capture, 21-50 break free
Choose Battle 2 times, Roll Dice: 1-20 KO, 21-40 capture, 41-50 break free
Choose Battle 3 times, Roll Dice: 1-25 KO, 26-50 capture