The key does not transport you anywhere; you must physically travel to the door which is color coded to it.
To reach the Gnomiverse with your key you'll first need to buy the key which is near the seagull inside Town Hall and then travel down into the deep sewer to unlock the massive padlocked door which sits across from the Chamber of Gnomes.
Travel through the Portal to the Gnomiverse and explore the outer edge of the area for four paths which will lead you to the various Doors leading to the different Trials.
When you approach the door for which you have the Key the lock will glow and when you get close enough you'll be prompted to unlock the door.
