First impressions are everything. Whether you are introducting someone or being introduced you need to be sure you are coming across in the best way. Hards rules of introductions seem to have gone away with the average person, but that doesn't mean you can't come across as who knows their etiquette.
Introducing Yourself: When you introduce yourself to others give your first and last name. Always be sure you stand up and introduce yourself. If you are wearing a name tag, be sure that name tag is placed on the right side so when you shake someone's hand they can clearly see it without having to look too hard.
Who To Introduce First: Always introduce men to women. For example you could say: "Mike Smith I'd like to introduce you to Mary Johnson." Also you should always introduce the younger friend to the older. Like any good rule there is an exception. If the woman has the highest title she is always introduced to everyone else.
Titles: If you are introducing someone with a title (such as a judge, ambassador, governor, senator) you should always use their title. Also continue to use someone's title till you are told otherwise. When you are introducing VIPs to eachother, introduce the one you know better to the one you may not know as well.
Whenever you are introducing people its nice to give a little background on each of the people. That will help the two connect and their own and have something to talk about if you needed to step away from the conversation.