1. Catching Pokemon
To capture a Pokemon you must first have your own Pokemon. Then you must go into a grassy area or a cave and walk around until a wild Pokemon attacks you.
You must then attack the wild Pokemon making sure you get it down to a small amout of HP, and make sure you don't make it faint.
After you have weakened the wild Pokemon you must use a Pokeball to capture it. Go to your items, and then choose a Pokeball, and hurl it at the wild Pokemon.
If you have weakened the Pokemon enlough it will be captured and you will have a new Pokemon on your team.
Remember: You cannot catch other trainers' Pokemon.

2. Pokeballs
There are many different types of Pokeballs. They all have different success rates and work better on different kinds of Pokemon. These are the main ones.
Pokeball - A tool for catching wild Pokemon with a normal success rate.
Great ball - A good ball with a higher success rate than a Pokeball. The chance of catching the Pokemon is multiplied by 1.5 times than using a standard Pokeball.
Ultra Ball - A better ball with a higher success rate than a Pokeball. The chance of capturing the Pokemon is multiplied by 2 times than using a Pokeball.

3. Evolution
Pokemon Evolution is when a Pokemon is ready to evolve into its next or final stage.
There are many different ways for a Pokemon to evole, including with experience, with evolution stones, by making it happy and by trading it.
If your Pokemon needs an Evolution Stone to evolve, make sure it has learnt all of the attacks that you want it to learn, because once you evolve it using a stone it won't learn any more attacks unless you use TM's or HM's on it.
Some Pokemon need to be traded to evolve. These include Haunter, Machoke, Kadabra and Graveller. If you evolve these Pokemon by trading they will continue to learn their normal attacks.
Most Pokemon however evolve by gaining experience. These Pokemon must level-up by challenging and defeating other Pokemon.
Some Pokemon must be very happy to evolve. You can make your Pokemon happier by keeping it your party, feeding it vitamins like Carbos and Iron and by giving it Haircuts and Grooming it.
Remember: You can stop your Pokemon from evolving if you press the "B" button while your Pokemon is trying to evolve.