You have to have the app actively turned on on your phone. As you move around your phone will vibrate when one appears. It is at random, heavily influenced by your real world environment, and appears on your phone. You can have a virtual reality setting that supplies a backdrop environment on your phone as you throw virtual balls on your phone to capture the animal. or you can have your camera turned on and it will place said animal on the image your camera sees.
Water pokemon appear near water. Sand/ground pokemon appear by deserts. Grass/forest appears in plains forest areas...so on and so on.
It is designed to get you out and exploring.
nearby buildings and landmarks of importance are given in game utility in the form of Gyms or "Pokestops". Gyms are to be fought over and controlled by you or other players. Pokestops give you in game items like health potions or Pokémon lures that attract (just increases your rate of appearances) pokemon to your location.
250 pokemon in the game now and future updates will introduce more. There is something like 1,000 all told.