First you must reach the part of the game where you're able to explore Cassell College's outdoor area. Here are the steps on how to change your look:
From your main screen, open up the map. You can access this by pressing the coordinates that is below the Wi-Fi symbol on the upper right side of the screen. The current map you're in will be displayed.

Open the map and head to the world map.
In the upper-right corner, below the wi-fi icon, tap the coordinates. This will open the map. On the bottom-right corner, tap the word map button.Head to Cassell College
Press the World Map button that's on the lower right section. This will provide you with a broader view of the places that you can visit in Dragon Raja.
Choose Cassell College, it's located on the lower right area. Once you have chosen this, it will show you the map of the campus.
The list of NPCs will be shown on the right side. Choose [Special] Class Transfer and you'll trigger Auto Find and go to his location.
Once you're talking to him, choose Change Class. You will be then brought to the class selection after and you'll be able to change your look from there.
You'll be able to view the class list from this window. Once you have chosen a class that you want, select it and you'll be prompted to another window.
Changing classes will cost you 300,000 Gold. After you've done that, you cannot change classes for 24 hours so take this in mind. The amount of gold you'll need is also quite high so make sure to save up.
As said above, the cost of class transfer will increase each time you switch the class. So make sure that you select wisely. If you are low on gold, you can read this Dragon Raja guide to farming & leveling.