Consider the existing features/furnishings in your home that you can't/won't be changing.
If the entry hall has a mottled rust tile, or the carpet throughout is a soft milky brown, while the bathroom tile is blue, and the new sofa you brought with you from your last house is a deep cherry red leather, then these colors are the starting point that must be considered in each of the areas where they exist. There is no use wishing it were otherwise, if you can't change them.
But if these are not your colors of choice, remember that you are not stuck with those colors alone. For example, say your family room (which will be getting the new red leather sofa) has a spectacular view of garden and green trees. You want to bring the greens and yellows of the garden in, you can start by finding a pattern (print or geometric) that combines the colors of the garden along with of red. Use that pattern on pillows for your sofa and/or use it in window treatments or upholstered chairs and you have accomplished your goal.
PROFESSIONAL TIP: Be sure that the colors you want to emphasize "read" from a distance. It doesn't matter that the red thread in the pattern is there if you can't see it from 10' to 12' away. When you consider a pattern, lay it out and stand way back. Quick! What are the first 2 or 3 colors you see from across the room? Those are the ONLY colors that matter for your purposes.