I've spent my January studying for a short Engineering Ethics class. I did a research project on GMOs and made a lovely presentation for the class. I feel like a illegitimate psuedo-expert on the stuff!
The main issue with GMOs in our food supply is that we have no consent over it. You're eating them. If you eat anything canned or boxed, you're probably eating GMOs. If you eat anything made with soy, you're probably eating GMO. 86% of our corn is GM'd. 93% of our soy is GM'd. Other countries are concerned to the point that they require labels or even BAN GM foods entirely in their country.
How are GMOs bad?
People don't like GMOs. There are several health reasons all speculations from correlations (allergy increase) & animal studies (more animals get sick or die when fed GM foods). There is one human study that shows there is some gene transfer (so the GM food genes transfer to your body's bacteria). The study seems really inconclusive of its significance. There are also environmental concerns. And the companies involved in this industry have pulled some nasty moves, but I'll just stick with the health.
How can I avoid them?
You'll hear a lot of people talk about GMOs negatively. And just say "don't buy them!" In order to make sure you're not being a part for the GMO industry, you have to make sure when you buy any of the food on the list or any food (processed or whatever) that has any of those derivatives as an ingredient says "GMO-free" or "organic". If you eat meat or animal products, make sure they are GRASS-FED and/or FREE ROAMING (not "free-range", yes "free-roaming") and organic.
I ain't got money or time for that.
Some of us aren't quite that hard-core about our food purchases. I, personally, feel that people who need to stay away from GMOs the most are those with food allergies and digestive issues. If you're serious about reducing your symptoms in regards to that, I really urge you to do your best to stay GM-free.
And with that, I leave you with this track :3