The first thing you need to do is choose a main color. This can, of course, be your favorite color (or that of the person being honored with the party), or a color that goes with the season or matches colors of other associated celebrations (such as with a wedding).
You will use that main color to decide what to use for accents. This is just like with any other form of design!
The easiest color schemes to make are monochromatic (different shades and tints of the same color), analogous (colors next to each other on a color wheel), complementary (colors opposite each other on a color wheel), and triadic (three colors equidistant on a color wheel). Here is an example, using a pink (#FF039A) as a base.
I used the Color Wizard on this design website to make my color schemes. (Bookmark it if you do a lot of design work, it comes in handy!) There are other options, as well, but I only used the more basic ones.
Use the colors you choose throughout the party, from the invitations to the cake, food, and decorations. No matter what scheme you use, it'll really tie everything together and show how much effort you put into the party.