To catch Pokemon, you need to have Poké Balls. To get them to to the Poké Mart or you can find Poké Balls on your way. Enter the Grass to battle a wild Pokémon. Weaken it down first, then select Bag when it's your turn again. Next, select Poké Balls and select Use. Then a Poké Ball will come flying out of the ball. If it captures it wll no longer shake. However, it will break free if it does not captures.
Does not shake = It might need a lot of weakening to capturing. Shakes once = You're on the right path, you could make it on a status problem. Shakes twice = Getting better, it could get captured with a better ball. Shakes 3 times = Almost! It might need Attracting, so it hardly attacks you. Shakes 3 times and does not shake again = You captured the Pokémon. Well Done!
"Will you give a nickname" will come up. Click on Yes if you want to, otherwise go underneath and say no. If you want a different nickname, go to the name rater's house in Goldenrod City.