Generally, one may be introduced by others or make self-introduction at the first meet. No matter being introduced or making self-introducing, the way should be nature not precipitate. When introduce a person, you should gesture politely by hand. Pointing with fingers is not acceptable.

There are sequences in introduction. You should introduce the young or people in low rank to the old or people in high rank; men should be introduced to women. When doing introduction all people should stand up except women and the elder. However this might be neglect at table. The introducee could just give some indication like smile or nod.   
Handshaking is etiquette when meeting or parting in most countries. On social occasion, handshake is not unusual. Generally handshake happens at meeting and introducing. Usually make a hold without effort. However the young or people in low rank should forward to show the respect to the old or people in high rank. Men only hold the finger part of women.

There are sequences in handshake too. Hosts, the old, people in high rank and women should offer their hands first. Guests, the young and people in low rank greet first then waiting for hands of their counter parts then hold them. Do not intercross while many people handshake at the same time. Wait till others finish their handshake. Men should take off their gloves and hats before handshake (according to western custom, people in high rank or women might handshake with gloves). When attending large-scale activity, for there are too many people, you could handshake with the hosts and greeting others with nodding, instead of handshaking. Soldiers with hat should raise their hands then handshake. You should look at your partner not others with smile. Some people from Buddhist countries in south and East Asia do not handshake, instead they close their hands to greet others. However we do not do this except we are treated this way. 

When meet acquaint ant people from distance in public place, generally you may raise your right hand to greet and nod. Hand-kissing and going down to ones knees are the ancient European etiquette, not often used at present