How to determine that a particular product is Organic?
The USDA does regulate a notion of "organic" in the US. Here's their full page on organic, and one specifically on regulations. Many of the links there are quite relevant. The best one for you is probably the labeling for consumers page, though many others would be informative for you as well. The Organic Labeling and Marketing Fact Sheet contains more details about labeling restrictions. Those pages all have tons of links, depending on what exactly you're looking for.

In terms of labeling, as described in the linked page on labeling, yes, the USDA regulates the usage of the USDA organic seal:


  Look at the label. If you see the USDA organic seal, the product is certified organic and has 95 percent or more organic content. For multi-ingredient products such as bread or soup, if the label claims that it is made with specified organic ingredients, you can be confident that those specific ingredients have been certified organic.


Unfortunately many other people do have their own notions of what organic means, and if you see the term used without the seal, then you can't really tell what standards it was held to.