All this combat will gain a character Experience (commonly called XP). Each monster you kill adds to your XP level. Once you have gained enough XP to advance to the next level(100%), you will see this in your inventory (The percentage can be different, of course):

Once we have gained this we need to do something about it.

We need to find a trainer, and there is usually once in each Town. The one in Dundee is named John, have a walk around near the town square to find him.

Click on John's name to get the training.

Click "Advance" to take you to the next level of skill and power:

So, we can confirm we have gone up a level, but what does it mean? Well, look at your inventory, and you'll see some changes:

Your HP, Power and Attack have all increased, and you get an extra Stat Point to spend on which ever stat you want.

Remember to visit a Cleric to take advantage of the new HP!

And that's it... all the basics have been covered. Click Finished if you have done, or click on Quests, Professions, or Guilds to learn more about other things in the game.