Each class has their own unique skill tree that you can allocate your skill points into. The skills at farther down the skill tree require that your character be a higher level in order to obtain.
A rough level indicator is visible on the left-side of the skill tree. Moving your mouse cursor over a skill will provide the exact level requirement, and any other skill requirements needed to unlock.
Up to three skill build tabs can be made available to allocate skills for different play styles. You can switch to other skill builds by clicking on the "Activate" button on that skill page.
If you want to reset your skill points, you can do so freely by clicking on the "Reset Skills" button. Unsure what skills to select? You can use the "Presets" to give you an idea of some ways to allocate your points.
Make sure to click on "Save Skills" when you are done!