I think it's different for everyone, but I always feel it if I'm about to faint. First, the back of my head and neck gets really hot and the warmth kind of spreads through my body from there. Then I get intense vertigo and nausea (think being really, really drunk) and my vision starts to get black spots and static. At this point (maybe 30 seconds from when I start to feel the neck warmth) I lose consciousness if I don't quickly get myself flat on the floor. If I can get down fast enough I usually spend about a minute lying there until I can see again and stop feeling like I'm going to fly off into outer space if I don't cling tightly to the rug.
I've only ever fully passed out once, as I get a bit of warning and always get myself horizontal asap, and I was alone, so I couldn't tell you how long I was out or how people reacted. I've had to lay down to prevent passing out at work, though, which is pretty embarrassing, but my coworkers knew I had "health issues" and I'd mentioned to them this happens with me sometimes so they were all really nice and understanding without freaking out about it.