A reliable method (if you are close enough) is to look at their eyes. Three of the four venomous snake species in the continental US will have slit pupils, these are all in the pit viper family. These are the Rattlesnake, Cottonmouth (Water Moccasin) and the Copperhead. The only venomous species you may come across in the wild in the US with round pupils, not a pit viper, is the Coral Snake. The Coral has a very strong toxin, but are not aggressive at all and prefer to keep out of sight. Usually when someone is bit by a Coral that person mistakenly tried to handle it thinking it was a Scarlet King.
There are of course venomous snakes in other parts of the world with round pupils like the Mambas and Cobras, but I'm just concerned with what I might run across here in the US.
BUT, just because a snake is not venomous, does not mean it won't try and bite you. Non-venomous snakes don't have fangs, but many species do have rows of tiny, sharp, little teeth and usually if they get a hold of you, they don't want to let go and you have to open its jaw and remove it with your other hand. Kind of like those little green lizards you played with as a kid in your yard would do, but just with a little more ouch! Just treat the little rows of puncture marks with a topical triple-antibiotic as soon as you can and you should be just fine. Common Water snakes and Spotted Kings are two snakes that I know are very defensive in the wild (don't really like to be handled) and will bite you even though they are not venomous.
Hope that helps.