First, buy from companies with established reputations. You may find vendors at fairs or flea markets, but they usually don't stand behind their products. Buy only oils stored in dark colored glass containers that have a solid cap. Oils stored in clear containers can be damaged by the sun and some oils can degrade plastic bottles and medicine type droppers.
If you are buying locally, check for dust on the bottles. Some oils will loose their potency over time. Open the bottles and make sure they smell nice. There can be a big fragrance difference between brands. You can test the purity of the oil by placing a drop on a clean piece of paper. If the oil is pure it should evaporate quickly and leave no marks on the paper.
When buying over the Internet, only buy a small amount the first time from a new vendor so that you can verify the quality of their oils. Try sending the company a question before you buy. If they don't respond to a possible customer, I wouldn't expect them to respond to a customer. Many on-line vendors will send you samples if you request them.
I have recommended the Essential Oil Starter Kit