How would I know if a food product is gluten free or not?

Even though a product does not have "gluten" listed as one of the ingredients, could potassium sorbate be gluten? How about potassium bisulphate? Or xanthum gum? How can I know for sure if a food product is gluten free?

Gluten can be listed as flour of unspecified type, wheat and derivatives, modified starch of unspecified origin (or derived from wheat or one of the other gluten-containing grains), malt, maltase, (malt anything), barley and derivatives, rye and derivatives, semolina, couscous, breadcrumbs...
Monosodium glutamate (flavor enhancer) may be derived from a gluten source, so should also be avoided. Soy sauce is made with wheat, so if it's in the ingredients, gluten is in there, too.
Xanthan gum is often used to replace gluten in gluten free food, and does not contain gluten. Guar gum is used in the same way.
If you were in the UK, you would just look in the "allergy" box, and that would tell you if gluten might be in the product.
Cornflour/cornstarch does not contain gluten. Herbs like rue do not contain gluten. Gluten is the protein in wheat, rye, barley, spelt and a few other closely related grains. It's not in corn, rice, or oats, although oats are mostly contaminated during processing, so you would need to buy ones that are certified gluten free (meaning they were processed in a gluten free environment).

Gluten is a protein. It is most often found, in some quantity, in grains, and is the protein that makes a grain "flexible". The best way to avoid gluten is to avoid grains and grain products, especially wheat, corn, and rye, which are the most common gluten products.
These days, though, you have to watch for other things that indicate that a food may contain gluten, even when it isn't grain-based. In general, you have to avoid anything that has "modified food starch", corn starch, wheat germ, hydrolyzed vegetable protein, malt, beer, rue, semolina (found in pastas), spelt, tabbouleh, teriyaki sauce (fermented wheat sauce), seitan, vital wheat gluten, pearl barley, matzo, malt flavoring, malt vinegar, kamut, hydrolized wheat protein, graham and graham flour, farina, farro, couscous,... the list is -huge-.
There are a couple of resources that can help. I like the Unsafe Gluten-Free Foods list at http://www.celiac.com/articles/182/1/Uns... for newcomers to gluten-free and grain-free cooking.