Basically religion in Civ VI works in steps. Accumulate enough faith (I recommend the policy starting out that gives you 1 faith per turn; it only takes about 10 or 20 faith if I recall correctly) and you'll be prompted to found a Pantheon. It's tempting to get extra build speed for Ancient/Classical Wonders or the Divine Spark which gives you Great Scientist and other points every turn, but occasionally it may be more advantageous to utilize the features around your city/empire (such as Dance of the Aurora if you have a lot of Snow tiles).
Next up, Great Prophets let you found a religion. You'll normally need a Holy Site District (when he appears you'll walk him over to the District and use his power) and enough accumulated Faith before one shows up, but you can get a Great Prophet automatically if you build Stonehenge (and it's a good way to found a religion and get a jump on the rest of the pack).
The next (and last) steps involve adding an additional two Religious bonuses, which are activated by building Apostles. You can't purchase Apostles with Faith until you have at least one Temple, and each one gives you the opportunity to add an additional bonus from the remaining pool of available bonuses. After this, Apostles, like Missionaries and Gurus, can be used to spread your religion around your empire and other cities and Civs.
The one thing about religion in Civilization that's important to remember is that, even if you're not going for a Religious Victory, the bonuses you can get (such as unique buildings like Wats that give you extra Science and Faith each turn, or bonuses to Gold, Science, Culture, and even Attack or Defense in certain situations) can make it well worth your while. It's also worth noting that the AI will, if given the chance, snap up the most choice of the pickings if you don't get to them first, so if you're going to pursue Faith at all you should definitely push hard from the outset of the game.
I'm sure I'm not alone in this, but beyond those early turns getting your bonuses established, it's pretty easy to let Faith become an afterthought in Civ VI. As others have said, it's probably nigh impossible for the AI to win a Religious Victory (and I don't even want to think about what it would take to do the feat yourself with all the opposing Apostles, Missionaries, etc. getting spammed everywhere), so after that you'll best be served focusing on other things like Science, Culture, and so on. In fact, you may never need to build more than one Holy Site; since Districts are tied to city population, it's a much better idea to build Campuses, Theater Districts, and other Districts that give you stacked bonuses toward a Victory type from then on.
One more little tip: you can manage the focus of each individual city in your empire (such as Gold, Production, Science, Culture, etc.) by tapping the Directional Pad to cycle through the little buttons in each category on your City screen. You can have the city focus more on one or two specific areas or even ignore one entirely (no idea why you'd ever want to do that, though). It's more intuitive with a mouse on the PC, but once you get the hang of it the Pro controller does well enough. Anyway, this can help you build stuff a bit faster or research Science faster or even provide more food for your citizens should you get an alert the city isn't providing enough food for them (another way to alleviate this is to make a Trade Route with another of your cities to get food to them).
Anyway, that's enough typing for awhile. Hope this can be of help.
