Some really good advice from a lot of people. I'll add mine, from the sellers perspective.
Some online shop owners really strive to make their pictures as accurate as possible when they're put online. In our case, we go to the manufacturers and get high-resolution pictures of the fabrics when we order them, then photoshop them ourselves to make sure they retain the correct color rendition when they are optimized for loading times.
If I can't get high-res pictures from the manufacturer, I do hi-res scans of the fabrics themselves.
Unlike equilter, however, I don't over-saturate the pictures and apply too much contrast correction. Their pictures are jazzy, but not accurate, and I'm looking for accurate.
I use an expensive color-calibrated monitor to make sure I am seeing exactly what is being put on the website, and compare those pictures to the actual fabrics.
Having said all that, here's what you can do to make sure you're getting the benefit of whatever work the store developer is putting into the process.
First, get yourself a decent monitor and get it calibrated for your viewing area. That will go a long way toward giving you the most accurate experience.
Second, I would recommend putting fabrics together that are from the same line, or from the same manufacturer. Many manufacturers have a standard color palette, and their blender lines cover this palette from which they create all their seasonal lines.
Third, when in doubt, call the store! Most store owners, especially online store owners are more than happy to assist you in putting together colors that will work with each other.
Good luck, and happy shopping!