How are you getting on? – just another way of saying ‘how are you?’

You doing OK? – asked when the person has had some tough experience recently and you want to ask politely if they’re OK.

Hi, …! What’s new? – this is a very informal way of greeting a close friend or anyone who you see on a regular basis and you want to ask has anything happened since you last met.

Hi, …! What’s up? – the same as above with a difference that you’re probably not that interested in what news the other person might have.

Hi, …! Long time no see! – used when you haven’t seen the person for a long period of time and you want to state that fact in the greeting.

Hi, …! Have you been keeping busy? – just a standard enquiry with little or no direct meaning.

Do you mind me asking…? – a typical way of asking something that might be a slightly personal question.

OK, here’s the thing … – a very handy way to start making your point if you’re not sure how to begin the sentence.