First you need to go to a map. Choose one from the home page or via Home -> Map #.
You can move around the map by clicking on the arrow buttons or simply by using the arrow keys from your keyboard. (Make sure the "Enable Keyboard Navigation" box is checked).
Click on 'Try to catch it' to battle it. You may have to weaken it before you catch it. Once you think it is weak enough, throw a Pokéball of your choice. Master Balls have a 100% success rate.
If the Pokémon was not caught, you may have to weaken it further.