Spirituality is simple: it's the feeling of being connected to something much bigger than oneself. It can be expressed as religion, as a spiritual feeling, even as knowledge and study; whatever connects you to the world around you in a positive way is spiritual. Finding your own spirituality can be as simple as allowing yourself to be drawn toward the things you enjoy and feel good about, or it can be as difficult as swimming through mucky water.
There are some people (and you know who these people are), who think they themselves are the greatest thing in the Universe. People like that are certainly not spiritual, and they are often insecure; often they have to coerce others to be like them, to do as they do, in order to feel better about themselves (though they'd never admit that). So those people will proselytize, meaning they will try to get you to believe as they believe. They often get very insistent about it. I once saw a YouTube video of two “Christian” girls insisting that a Hindu girl from their school become Christian. It was interesting that the two Christian girls knew absolutely nothing about Hinduism, about the Indian subcontinent and its cultures, or about the other girl's beliefs--they just “knew” that everyone has to be Christian.
People who are secure in their spirituality are not like that. They do not need to tell anyone else who to be or who not to be.