Basically the game consists of running around and gathering resources. Some of these resources, such as trees, crops, herbs and animals are created, placed and destroyed by the players. Usually there's a 'war' going on between people who only want one kind of tree in one place, poisoning all other trees and stuff.
Skills are learned automatically, even while you are not playing. You simply select the skill you want and wait. The more skills you have and the more difficult the skill, the longer it takes. You can donate stuff to the Giants related to the skill to shave off some time.
You can then use these skills to gather resources more effectively, or learn skills that allow you to create various items and foodstuffs. These help you maintain your energy and mood, and you can of course sell them for a profit. Every 4 hours counts as an in-game day and resets your energy and mood and lets you re-harvest trees and animals you harvested the previous day.
Locations in the world are called 'streets', and the creation of a new street involves the players gathering resources to finish the project. You get achievements for it I guess. From what I've seen players don't get to influence the look of the street in any way, they just get to plant trees in pre-designated spots and release piggies, butterflies and chickens to populate the area.
Other events are 'Rook attacks', in which the Rook, giant evil birds, try to destroy parts of the world. Players can gather and use certain skills to repel these birds, unskilled players can help provide power by donating stuff to the shrine in the attacked area.
Other than that you can just do whatever. Most people get a house so they can keep their own piggies and chickens and plant crops and trees in their private garden. You can try and earn lots of money or perhaps unlock all recipes, get lots of achievements, collect certain items, stuff like that. People seem to like hiding random stuff around the world to share with others, or leave fun notes, or rename all chickens to 'Dinner'. If you come across a chicken named 'Curry', I was there. Curry is my RL chicken.
A common misconception is that this is a Facebook game. It is not. While you can link the game to your FB account, it is no different than linking it to your Twitter or something. No part of the game at all requires or even allows your friends to click anything to help you, the game doesn't post anything to your Facebook unless you tell it to, which you don't have to at all.
It is also completely 100% free to play. You can use real money to get fancier clothes and facial features for your avatar and buy teleport tokens, but that's it. With sufficient teleport skills you won't need those tokens, and running from point A to B is usually quite easy and often lucrative if you harvest a little along the way. There are absolutely no other ingame benefits to spending money.
Frankly, it's a good game but I don't see most of the people on these forums playing this. I don't want them to either, the piggies are all mine. Mine!