It is possible to improve your skills beyond what you chose at game start. During turnsheeting, you can can take training actions. These will grant you Training Points (TP), which you can spend on upgrading an appropriate skill.

Training Points Upgrade
2 Gain a specialization
4 Learn a new skill at level 1
6 Upgrade a level 1 skill to level 2
8 Upgrade a level 2 skill to level 3

You can gain TP in one of the following ways

Practise

For 2AP, you can train yourself in a particular skill. Naturally you need the means to train, namely somewhere to practise, and the appropriate study aids (a sword, a tome of lore). You get 1TP from this.

Ulrik fancies himself as an Adventurer, so wants to improve his anthropology skill. His friend Nasha has allowed him to visit her museum, and study in her library. So he spends 2AP on Practise (Anthropology). He now has 1TP in Anthropology.

Learn From Others

This works similar to Practise, except it costs 1AP for the tutor, and 1AP from the trainee. You get 1 TP from this.

Ulrik wants still has a ways to go, so he persuades Nasha to tutor him in ancient artifacts. Nasha agrees to give him a personal tour of her museum, discussing the contents in depth. Nasha spends 1AP on training, and so does Ulrik. Ulrik now has 2TP in Anthropology.

On the Job Training

The best way to learn is through experience. While working on any other task, you may spend an additional 1AP to train in that area. For each 2 AP you spend doing something, you can add an extra 1 AP to train that skill and receive 1 TP.

In exchange for her services, Nasha persuades Ulrik to retrieve an artifact from the Temple of Relative Succour (a most foul place!). Ulrik agrees, seeing it as a valuable opportunity to test his skills. He spends 4AP on venturing into the temple. He then spends 1AP more on On the Job Training. He now has 3TP total in Anthropology.