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.
Precedence and respect is signalled by the name said first. Courtesy gives honour to those who are female, older or more distinguished.
Address the more senior person by name and say: ‘John, may I introduce Charles Berkeley? Charles, this is John Debrett.’ You may wish to then add a short explanation, or provide some information: ‘John is a wine expert’, or ‘Charles has just moved back to London’ or ‘I know you are both tennis fans.’ It is helpful to give both first name and last name, even in an informal setting, as it provides more information, which is the object of the exercise.
Introduce individuals to the group first and then the group to the individual. For example, 'Mary, this is Jim Wilson, Bob Aspinall and Sue Godstone. Everyone, this is Mary Debrett.' Married couples are introduced separately, although it is advisable to clarify the relationship ('And this is Sarah, Peter's wife…'). 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). With younger people and in more informal settings you may prefer: ‘Hello’ or even ‘Hi’ but resist adding: ‘Pleased to meet you.’