Patty, when I am looking at fabric I will hold the fabric up to see if I can see my hand through it. If you can, it means the weave is looser and the fabric will shift more and probably fray. Another thing to check is the "feel". Quality fabric should have a smooth feel, not lumpy or knotty. You can take the fabric in your hands and check it for stretch, both on grain and on the bias to see how much flex it has (again you are looking for a tighter weave so not a lot of flex, though bias will always have flex to it). Another thing to look at is the print - rub it with your fingers and see if any dye rubs off. Is the pattern printed straight and is the printing evenly colored throughout? These are some things you can look for when checking fabric for quality. Generally speaking, if you are shopping at LQS you will have only good quality fabrics being offered. But if you go Joanns or Walmart or another big box store, you can check the fabric using these guidelines.
Sorry for the long response. I am really picky about my fabric, so I don't buy from Joanns or WalMart. I would rather buy less, pay more, and get good quality from my LQS. Hope that helps!
I can't buy online either, because I have an elaborate petting ritual I must observe when fabric shopping :lol: But if I have one in hand I like, I will reorder it online if I need to.