When decorating with an adjacent color scheme the best place to start is by either choosing your favorite color or deciding on the mood of the room. Cool color will give your room a cool and relaxing feel. It also has a tendency to sometimes make the room appear more open and airy. You may want a warm and cozy room.
You want to first decide on what kind of feel you want your room to be... warm or cool. Then choose a color you like. So, for example let's say that you are decorating a bedroom and you want a cool calm and relaxing feel. Choose from the cool colors on your color wheel... which would be blue green and a cooler violet or purple.
For example... say you want blue to be the dominant color in your color scheme... then you can choose colors that are next to that color blue on the color wheel as accent colors in your room

So, in this example of this bedroom... you see that the cool blue grey is the dominant color in the room. It is dominant because it's the color on the wall and on the bedding. But you also see a cool muted green... on the bedskirt and pillows. You see the same cool green in the draperies. You would find that muted green right next to that cool blue on the color wheel.
This is a good example of an analogous color scheme using cool colors of blue and green. You may also notice that the designer had a little fun with this color scheme and added a bright blue chair. The blue chair works because it is still in the same family of blues and greens.
The decorator could have taken this scheme even further with the colors... by going further along on the color wheel... getting closer to yellow or even over to a warmer blue as accent colors. However, you may lose some of the relaxing feel of the room.
The tighter the color range on the color wheel for your adjacent color scheme the more calm the room will appear. The more colors and wider range of colors on the color wheel you use for your adjacent color scheme... the more vibrant the room will feel. This decorartor uses muted cool blue as the dominant color... and muted cool green as the accent color. For the neutral colors in the room you see some off-white and white and wood tones to balance the room out. With almost any color scheme... you're going to use some neutral tones. White is an excellent choice for a cool and relaxing room