Let's go ahead and break down what this menu is showing us. 

On the far left hand side, you will see all available skills. Hovering over them will give you the skills name, a brief description and level requirements to use it.

If you do not reach the requirements for the skill, then the text for the level requirement will highlight red.

Let's move on over to the rightmost side of the screen now.

Below, you will see the column for unlocking and upgrading each skill. Which skill is being upgraded depends on which skill was last selected, on the left hand side of the menu shown above. 

As previously mentioned, all skills may be levelled until level 30

Lastly, we have skill slots.

We have a total of 6 Main skill slots and 2 passive skill slots

The icon will change once a skill has been assigned to it. Hovering over it will identify what skill is currently in that slot.

To bind a skill, simply select the skill on the left hand side and then click on the slot that you want it in.

To cast a skill, press the [F] key. If this key does not work for you, you likely rebound your 'Swap Item with Offhand' button. See below to find out which key is bound.