Compare it to a legitimate copy
The easiest way would be to compare it to copy that's known to not be a counterfeit. To start with you might want to look at some pictures of the box on board game geek and see if there are any differences. As with other counterfeit things, looks for misaligned printing, coloring that is off, or other differences. Due note though, the picture I linked to is from the Kickstarter, and the retail boxes might be different (look at the amazon/etc listings and compare those pictures too!)
If it externally looks legit, it could still be a fake; to know for sure you'll need to open it up and actually look at the contents. Are the cards very flimsy? Misprinted? Miscolored? Is the packaging "weird"? My copy came with each deck in shrinkwrapped plastic, if the decks are held together with paper slips, or rubber bands, or not at all, that's a sign it might be counterfeit. For games aside from Exploding Kittens, check other components too... Are pawns made of plastic when they're supposed to be wood? Are they the wrong shape/size?
Ultimately though, it might not be possible to tell just by examination, you may need to find out where the store bought them, and follow the distribution chain to see if it actually leads back to "The Oatmeal" or not. It doesn't hurt to ask the store WHY the item is so cheap compared to MSRP.
For $10 I wouldn't be surprised if it was a) counterfeit and b) made with cheaper materials.
All of that said, do also keep in mind that often times Kickstarter versions of games (which you'll frequently see in pictures on BGG) have better quality components than those that are included in retail versions, so when comparing pictures make sure you are indeed comparing retail to retail (or KS version to KS version).