Decide how much you want that red couch to be a feature in the room. If you REALLY love the color red, and you want to create the illusion of a bigger room, you can paint the walls red and the red couch will blend in! However, if you prefer to make the couch a feature in a more balanced room, and believe an all red room is just too much of a good thing, move on to step 2.
Determine if your couch is a warm red or cool red. A warm red is closer to orange than purple. On the flip side, a cool red is closer to purple than orange. This is going to help you determine your color palette. If you’re not sure, and you need help determining the tone, hold a sheet of white paper beside the couch, and look at the part that's beside the paper. Since white is the most neutral color, you should be able to tell if it’s closer to orange or purple. If you're still unsure, simply bring some of the following paint samples that appeal to you home to place near the couch to determine which looks best. A warm red couch will look nice with colors that have a lot of yellow in them, like warm browns/beiges, yellow, sage or olive green, or rust. A cool red couch will look nice with colors with blue in them, such as violets, blues, or cool greys.
Think about the mood you want for the room. Do you want it to be calming? In this case, choose a medium or even darker shade of the above colors for the walls in the room. This is because reds are usually medium or dark colors, so there will be less of a contrast. For a more vibrant, dramatic mood, choose a lighter color for the walls than the couch. Follow this same principal for your flooring, and/or the area rug you use in front of the couch.
Follow your sense of style. Some colors are more traditional, while others more modern. This will narrow your choices further from step 3. For a warm, calm, traditional room try deep beige or olive green. For a warm but vibrant traditional room, try cream. For a warm, calm, modern room try light beige. For a warm but vibrant modern room try apple green. If you'd like a cool, calm, traditional room, try grayish blue. For a cool but vibrant traditional room, try lavender. For a cool, calm, modern room try medium grey. For a cool but vibrant modern room try yellow or apple green. Again, paint samples can really help you see which colors YOU enjoy together. Use the above advice as a guideline.
Choose no more than half of your accessories in red colors to coordinate with your couch to create a balanced look. Good luck!
If you don't like your red couch, and you're researching how to decorate because it's a hand me down, ignore all the above advice and slipcover it! ;)