Always give a little eye contact to the people you clink glasses with.
Eye contact means you're celebrating the person holding the glass, not the glass containing the drink. It's not a big issue if you don't make eye contact, but if you do make eye contact, you'll receive an esteemed look from your counterpart because they'll know that you know.
It's all in good fun. I didn't start making eye contact for a Cheers until I was 30 when my friend said "Eyes, eyes, eyes, eyes, eyes, eyes!" to me and explained the whole thing. I've been participating in the eye contact Cheers ever since.
I almost laugh every time someone gives me that esteemed look because it's as if we know something the others don't, even though it's nothing.
If a toast has been made, or someone raises their glass to yours, it's expected you will drink from your glass. Not doing so is considered slightly rude, but not always.
Let's be honest, when a table full of people say "Cheers" and you all clink your glasses together and everyone drinks except you, it's probably not going to start a conflict, however if someone raises their glass and looks you in the eyes they'll be expecting the same.
The toast, or cheers, goes way back when strangers would drink together. A certain trust would be shared by splashing some of your drink into theirs, and their drink into yours.
This splashing of liquid into each other's glass is followed by a gulp to ensure one has not attempted to poison the other, and thus trust is established.
Very old traditions, I know, and perhaps unnecessary, but once you start making eye contact while saying "Cheers", you may never look at the glass again. Cheers!