There’s a bit of confusion about how the character class skill trees work in Destiny. For starters, there isn’t really a skill tree in the traditional sense. Instead, there’s a skill sheet made up of ‘core’ skills and skill sets.
Essentially, no matter which class you choose (Hunter, Titan, Warlock), you're given main or core skills. You're able to select all three of them, and you'll always have them. The other skills essentially allow you to unlock them all, but you can only use one per vertical column.
As you play, you can unlock all of the skills, however you will need to choose a build and in all cases select only one skill per green skill set column. It’s a bit like choosing a rune for your skill in Diablo 3.
In addition to your regular skills, there are subclasses that are essentially skill trees that you equip and level separately. You only gain experience in the subclass you have equipped. Each subclass gives you a different Super and has a specific type of damage that all of its abilities deal.
The picture above feature the Gunslinger subclass and was the only Hunter subclass available during the Destiny alpha. Every upgrade you see in the picture is within the Gunslinger subclass itself.
Other subclasses will be available later in the game and you can switch out the subclasses at will, much like you would any other item on your character.