... it's not really an it, is the thing. There's not exactly one sort of faith, or one sort of expression of it. Even remotely. If you're looking for something approaching a commonality... just get into meditation and/or self-hypnosis. Do some research on religion-centered oration and how priests have preached throughout history, the cadences and settings and methodologies and whatnot that they use to get folks to listen. You don't have to have a religious component to put yourself into the mindset of many believers when they're having a religious experience, just perform the right actions in the right environment. Without a doubt that would be the most common mechanisms, dressed up in religious regalia or not, to experience what most people seem to consider faith. But if you're looking for a singular answer, a definitive "this is faith and what it feels like", you are barking not just up the wrong tree but in actuality yodeling at the roots of a fern in the wrong forest. Not just not in the ballpark but in fact lounging in a cave in a different galaxy as the ballpark.
Personally, the closest I've gotten to a religious experience -- faith more pronounced than just the idle belief that the ground isn't going to fall out from under you in normal conditions type stuff -- that wasn't easily identifiable as an outright psychotic (well, major depressive, whatever) break came initially from music (at this point I can largely induce the same thing with a shift in breathing and a little attention, but that's neither here nor there). The sensation of losing yourself to something else, of subsuming what you are into something that's patterned in a particular way, of narrowing your focus down to the sound and yourself and naught else... it's the same thing many folks feel in church or whathaveyou, by and large. Add in that good ol' ASMR for an additional physical reaction and it's a feeling of faith by any means except the claiming of it. Bit of disassociation, altered cognitive/perceptive state, bit of physical feedback and a sense of overall release/relaxation and there you go.
Other folks get different things, or identify different mindsets as ones intertwined with faith. I've talked to folks that felt they experienced faith most intensely in moments in incredible terror (or awe in the original, holy shit that mountain is on fire and falling on me, sense), usually accompanied by what they claim are visions* -- a sort of absolute knowledge that you are in the presence of something able and entirely willing but for <Reason> (usually contingent on their religious beliefs) to utterly destroy them. Others that broadly speaking don't feel anything outside of the norm, but ascribe to faith what others would call simple conscience -- that little voice in your head that tells you how to not fuck up, given metaphysical weight. Still more that claim a sense of presence and companionship as they speak with holy figures (usually in dreams, sometimes just via good ol' hallucination), or the sensation of something being with you (usually something related to their spiritual beliefs) in some sense or another.
The list just kinda' goes on... to a degree, just as you can view things as there being a different god for every individual (no two people that claim to share beliefs really interpret them the exact same way; all who hold belief can be said to actually be a member of a religion of one, that happens to share somewhat superficial similarities with certain others), there's a different faith for every believer... even another sort for all but the most incredibly insane of non-believers, too. The simple unattended confidence that the sun will rise in the east is a sort of faith, too. Different from most religion related ones, but eh.
*Perhaps unsurprisingly, I just call them hallucinations if I'm not moderating what I say to make sure they're not going to flip out and try to kill me, heh. I've had the same experiences, but don't ascribe the same interpretation. The human brain is really rather incredibly good at going haywire to one extent or another, and acknowledging that has kinda' been important for me, considering I've been hallucinating 24/7 as long as I can remember.