Catching Pokémon

Obtaining Pokemon in the wild involves two processes, Tracking it down and Catching it in a Pokeball.

Tracking
There are a couple ways in which Pokemon can be found on the world map. Sometimes they randomly spawn immediately in range of your location, which can be encouraged with incense and lures. And sometimes they spawn elsewhere on the world map, waiting for a trainer to track them down with the help of the "Nearby" tab. (screenshots pending)
 * 1) Footprints (an indicator of the potential distance between the Trainer and the Pokemon)
 * 2) Blue Ring (indicates the Pokemon you are currently focused on tracking)
 * 3) Silhouette (indicates a Pokemon you have not yet registered in your Pokedex)

Footprints
The footprints in the Nearby tab can give you an idea of how far away a Pokemon is, and whether you are moving towards or away from it. Zero footprints means you are within catching range, 1 footprint is just outside of that range, 2 and 3 footprints means you are farther and farther away. If a Pokemon you are tracking changes to zero footprints, simply stop where you are and wait, it will appear on your world map in a few seconds.

Exact distances have not yet been calculated, but two things concerning the footprints are generally accepted. Zero, 1 & 2 footprints all seem to indicate the same distance, regardless of the Pokemon being tracked, while 3 footprints can indicate a variety of ranges possibly depending on level of the Trainer, the CP or rarity of the Pokemon, or other factors yet to be determined. (link to forum discussion pending)

Blue Ring
When you tap on the Nearby tab, it opens up to show you any Pokemon in range. Tapping on a specific Pokemon in that screen will make it the focus of your interest, and change the Nearby tab to show just that Pokemon and its footprints indicator. Opening the Nearby tab again will now show that selected Pokemon with a blue ring amongst all others in range. This can be helpful in determining your distance and direction from the target Pokemon since you can now see it relative to the other Pokemon in range. (screenshot pending)
 * 1) Pokemon closer to you than the target
 * 2) The Target
 * 3) Pokemon farther from you than the target

Catching
Once a Pokemon is visible on your world map, you may attempt to catch it in a Pokeball. Tapping on the Pokemon will bring you and the Pokemon into the capture screen. (screenshot pending)
 * 1) Background (varies based on whether you are playing with AR on or off)
 * 2) Difficulty Ring (green,yellow, red)
 * 3) Pokeball In Use
 * 4) Items