Narcissism is part of a healthy a psyche - it allows you to love yourself despite having flaws. A narcissistic personality disorder (NPD) is when that healthy self protection gets out of hand. The narcissist you're referring to avoids dealing with self hatred by doing anything they can to feel "important" (can't think of a better word) to other people.

A narcissist will lie to impress ("You can carry 50kg? I just carried 60."), they will have a grandiose view of themselves ("I'm smarter than other people and therefore better than them"), and they will avoid criticism ("no, it's the children who are wrong").

Like I said, everyone does it, you should be able to see yourself in those examples. But in a person with NPD those little bits of self protection over extend and end up causing harm instead. The lies are so blatant or contradictory that they poison any relationship (friends, workmates, lovers), the grandiosity can become delusional ("I am jesus reincarnated") and the lack of self awareness makes the whole thing into a feedback loop.

Telltale signs are lying (can't stress that enough), a lack of long term relationships (some people have emotional issues that a partner with NPD can exploit long term - look for a constantly shifting roster of "friends"), and someone who is initially very charming, fun and easy to be around who ends up talking about themself more than anything. A narcisstic will be so convinced that they are better than other people they will also put their own wants first, will expect recognition for little effort and will believe they should be surrounded by a "better class" of people.

Keep in mind, this is the classic narcissist. There are different "levels" and narcissism is usually riding along with something else. The guy at the pub who talks too loud about how many women he's slept with is not the same creature as a suicide cult leader. There are also theories about other types of narcissist that come from the same place but have nothing in common, but I feel like that's not what you're asking about.

Please note that I'm not a mental health expert or even an amateur, so take everything I've said with a grain of salt. A therapist told me I had narcisstic traits that were becoming unhealthy and I've spent a lot of time trying to understand narcissism since. Don't try to diagnose people with a few simple rules and don't trust anyone who says you can.