As much as you like to believe in redemption, first impressions are critical to second chances--at least in the friendship and social interaction world. When you are seeking new friends, you must obviously make an effort, but the initial effort is the most important.
You need an opener. You need to find some friendly, comical, welcoming, warm, or caring way to make that first impression upon a potential friend.
Look for ways to relate to someone without creeping them out. Be observant without being intrusive. Compliment someone--their hair, their clothes, their home, their laugh, their smile, etc. Present your compliment in a casual way. Don't ever force a compliment on someone. It should feel natural to the situation.
Again this is something to work on or put into practice before you can feel comfortable having a good opener in seeking new friends. You may have to fail a few times, endure some awkward moments, or even creep someone out. Take heart though because this will be beneficial for you to experience and funny for you to laugh at afterward.
OH...and always introduce yourself. Before or after your opener will suffice. Be accessible to your potential friend in the nominal fashion.