If you are the link between people who have never met it is up to you to make the introductions.
Never neglect to do so; it makes people very uncomfortable to be left standing on the periphery, while you engage in animated conversation with a stranger. Remember the hierarchy: men should be introduced to women, juniors to elder people and higher ranks.
Introduce individuals to the group first and then the group to the individual. For example, 'Mary, this is Jim, Bob and Sue. Everyone, this is Mary.' Married couples are introduced separately, although it is advisable to clarify the relationship ('And this is Sarah, Peter's wife…').
Unless the occasion is formal there's no need to mention surnames, although the use of surnames is more common amongst members of the older generation. If possible, offering a little information about each person as you introduce them ('Rupert and I were at school together') will help to break the ice. Speak clearly and don't mumble; you don't want people to be left embarrassed, forced into 'I'm sorry, I didn't catch your name' excuses.
If you are introducing people with titles, err on the side of formality (especially for the older generation) and use 'Lord' and 'Lady' much as you would use 'Mr' and 'Mrs'. Don't use the full title (the Marquess of xxxxxxxx) in conversation; this form of address is used for formal correspondence. It is up to people with titles to terminate the formality with a simple 'Just call me James…'
When you are introduced, the traditional response is 'How do you do' (this is a salutation not a question, and requires no response - just say 'How do you do' back). To many people this sounds over-formal, and a friendly 'Hello, good to meet you' is becoming the standard response.