Somebody updates their facebook status.
I think you just know. I've typically been in relationships without dating, so I'm dealing with the same thing right now. I don't "feel" I'm in a relationship, but I think I might be.
After sex, I think you are in a relationship.
If you have an unspoken agreement to do things with the other person, that's also a relationship.
If you have a prerogative for open contact at all times, that also seems like a relationship.