All you have to do is swipe your screen to throw the Pokeball. When you see a wild Pokemon for the first time, there will be a color indicator surrounding it, which shows how hard it will be to catch. Green is the easiest level; orange indicates a medium level and red, of course, being the hardest to catch. To have the best chance at catching it, press and hold the Pokeball and the capture ring will begin to shrink. You will want to practice on the green ones to make catching the orange and red ones a little easier.
You can also use berries to make capture easier, thus changing the color of their ring. If a wild Pokemon has a question mark in place of its CP rating, this will be too powerful to catch. Save your items and move on to something else for now. You can always come back to it later.
There is a bar at the bottom of the map screen you can tap on that will show you your proximity to nearby Pokemon. The slots indicate their closeness to you: slot one will be the closest, slot 9 the farthest away, etc. You can tap on the Pokemon you want to capture and look for footprints on the map to track them down.
Once you have captured the Pokemon you can view their stats by tapping on the Pokeball. You can view their attacks, move them into types and choose how to organize them this way.
Trading of Pokemon is not available yet, but is planned as a release in the near future!
Step 1: Get Started