You can add a new skill line to an open circular slot at the side of one of your attribute rows. To do so, you must visit a trainer during a town encounter and choose a faceup skill line token there. The new skill line must be placed in an open circular slot at the left or right end of a row.

Note that a new skill line (after the start of the game) starts with no dice, as you need XP to get the skill dice.