If you are with a friend and run into another friend who doesn't know the person you are with, you might say Janie, this is Susan. Susan, Janie. You also might share something about the relationship such as the fact that you work together or attend the same gym or whatever.
To introduce yourself to a stranger, merely say hello and say something very general to the other person about the weather or what is going on around you to strike up a conversation. Sharing too much information with a stranger is not wise. Many a person has regretted sharing too much information too soon. Personally, I don't like to listen to too much information from someone I hardly know unless I ask. It can be very uncomfortable.