Patch 1.3 in Stardew Valley added a statue to the game that allows the player to change their professions, which was one of the most requested features for the game at launch. This is now possible with Patch 1.3 (some consoles have not yet had the 1.3 update at the time of writing this guide), and all you need to do is to head to The Sewers and interact with the Statue of Uncertainty.
If you don't have unlocked the Sewers yet, go find 60 different items to donate to the Museum to get the Sewer Key.
The Statue of Uncertainty looks like a statue with a dog's face on it, and you need to interact with this. You can pay 10,000g to chance skills for one of your professions. After paying, go to bed, and you will first select the level 5 skill, and then promptly select the level 10 skill right after that.
If you want to chance the skills for more than one profession, you will need to do it on different days, and pay 10,000g per profession you want to change.