The three critter-things surrounding you were Charmander, Bulbasaur and Squirtle. They are what are known as "Starter Pokémon", a Pokémon given to you for free at the beginning of the game to get you started on your adventure. Everyone who starts a new game of
Pokémon Go will get the same three critter-things, but you only get to choose one. Of course, through playing the game, you can eventually catch the other two.
At this point, your task is to travel around, visit PokéStops
(shows as blue circles on your map) and Pokémon Gyms
(shown as red, blue, yellow or grey square-shaped buildings), and catch the various Pokémon that you come across along the way. For every Stop you visit and every critter you catch, you will gain experience points and level up, allowing you to catch new and stronger Pokémon. Additionally, once you reach level 5, you can start battling the Pokémon you have caught at Gyms. You will be required to choose one of three teams; Team Mystic
(blue/water), Team Valor
(red/fire) or Team Impulse
(yellow/electricity). When visiting gyms defended by your team, you can train your Pokémon there and get used to how battles work. When visiting an opposing teams gym, you can attempt to defeat the defending Pokémon and take over control of the gym for your team. As of this moment, this is about the extent of what the game has to offer.
Eventually, through future updates, additional features will be added. Trading Pokémon with friends and passers-by, battling Pokémon outside of gyms with friends and passers-by, and limited-time events to catch rare or legendary Pokémon are just some of the features that the developers have already revealed to be on the horizon.