It seems that most knitters are comfortable with analagous colors, the colors that are next to each other on the color wheel. They are "safe" colors to put together... hardly anyone could find objection to seeing them together as long as they liked those colors individually. Green, blue, and purple are analagous colors, as are red and orange, for instance.
Such "safe" groups of colors may be the route you want to take when knitting for someone at the office or a relative. But since one of the benefits of hand knitting is that you can put together colors that uniquely express yourself and that you might not find "everyone else wearing", it's sometimes satisfying to branch out and try something a little different.
Color Wheel Turnings
If you're not sure where to start, pick up a color wheel, preferably one as shown here (Johannes Itten) that has a series of black cover sheets that isolate the different color groups, such as this split complement. You don't need to know all the terms for the groupings, but if you play for a while turning each one of the black "isolators" around the wheel, you'll find some pleasing color groups that you might not think to put together on your own. Yet, based on color theory principles, if you combine any of the colors identified by these black discs, they will work well together!
This afghan resulted from discovering a "triad" (which I didn't like at all at first) that I discovered when "playing" with the color wheel this way. The triad was of orange, purple and green. So I experimented by felting a rug for my puppy's crate using purple orange and green. And, to my surprise, I liked it! So then I put these odd skeins of Colinette together using the same triad and knit up a variation on their feather and fan throw.
I also would never have thought before of putting blue and orange together, but experimenting with the color wheel and complements led to this cardigan and the little shots of blue-violet here and there make it much more interesting.
Another exercise that I learned from weavers is to do "yarn wraps". Weavers say you should "do a wrap a day". So first you need to cut a bunch of 1-2" wide strips of cardboard. Then put all your yarn scraps out on the table. There are several approaches to this exercise, as outlined below, but in each case, you'll tape the end of each color to the back of the cardboard and wrap the yarns around the cardboard, snuggling them next to their neighbor. Doing these really helps you see colors together in new and different ways. You won't love every wrap you do, but you'll learn a lot from it and they're quick and easy, low risk ways to play with color.
Here are some versions of how to approach "yarn wraps":
1) Pick 3 yarns/colors that you think you like and wrap them in equal amounts in a symmetrical arrangement. Then wrap them randomly. Then wrap them using the Fibonacci numbers. Then assess each one and see which you like best.
2) now, pick up a color from the opposite side of the color wheel from the colors you wrapped in step 1 above and wrap this color in along with the original colors and see how you like it. Now vary the amount or proportion of each color used and see how you like it.
3) you can also start by picking 3 colors you don't like together, or if this is hard, either pick yarns with your eyes shut or do this in a group as follows: each person picks 3 colors they like and then keeps one and passes 1 to the person on their left and passes the other to the person on their right. So now each person has one of their original yarns plus 2 they've inherited from their neighbors....not usually a pleasing group of 3 colors (unless you and your neighbors all gravitate to the same colors!). Now each participant picks out 1 more yarn from the center pile that they think will help "bring together" the 3 yarns they have.