The best way to give a self introduction is to explain to the people you are introducing yourself to what they should know already. If this is a job or college interview, expand on the CV that they have already seen. Just tell them how you got to this place in your career and where you wish to be going forward. This will show your skills that you have written down and also the skills you possess in being able to expand on a point, as they will know that you can explain where you are and also add in a bit of personality. They will be able to see that you are more than what they have written on their piece of paper about you.
Make sure that you point out all of your good qualities and make sure that if there is anything they already know about you, you acknowledge this and make them feel comfortable that what they already believe is correct.
You should outline the reason why you are there giving this introduction, what drives you to become a part of their workplace of college. Make sure that you are always polite when talking. One of the most important things to do is not to swear and not to use any kind of slang. It's ok to use abbreviations, especially if they are abbreviations associated with their business.
Ensure that at the end of your self introduction you ask them if they have any questions for you and then that way, if you have left a stone unturned and they would like to know more, they can always ask you.