Often, one is given a “must” color to use. Usually it revolves around the company logo.
You need to come up with a support color palette around that.
Sometimes, you have complete control of color.
Define what the overall mood should be, happy, modern, techy, established, earthy, conservative, etc. This will help determine color palettes.
Observe color palettes from other artists. Observe the colors around you, in nature, wallpaper, clothing, interiors, etc.
There are some books out there which have color combinations.
Create a page in your image editing program. Fill the entire page with a color of your choice. Make a small rectangle and fill it with your secondary color. Create a 4 pixel line for your third color. Adjust all of them until pleasing. Take your time!!!