While layering different styles makes a home interesting and can save big bucks in the decorating budget, do keep in mind just a few simple tips:
First, have a common element - like colour or scale of furnishings. For example, if you have lots of colourful items in the room, think about using white as your backdrop. (You know I'm always going to advocate for white walls, right?)
Second, make sure to spread the styles around, hence the word "mix"! Don't have only one room in the house, or worse, only one half of a room, completely traditional and the rest completely modern. Seems obvious but make sure to step back and survey the space to make sure you've weaved the elements together.