It's important to remember the following points:
You should always approach each situation in a non-judgmental way, as you won't know the 'whole story' or the person's circumstances. You should treat the person with tact and sensitivity.
What should you look out for to prompt you to raise an issue? Does someone appear ill, perhaps you've noticed that they're struggling with a cough, this could enable you to raise the issue by asking a simple question, such as "that’s a nasty cough, have you had it for long?" You can then judge whether or not to continue, depending upon how they've responded.
Look for signals
We all give out signals about how comfortable or uncomfortable we feel about a conversation. What signals do you give out? You should be friendly and approachable, using an open posture to demonstrate you're interested and ready to listen / help. This all helps to build a rapport with someone.
Watch to see how someone responds to you. Were they listening intently, leaning towards you and maintaining eye contact? If so, that's normally a green light to carry on with the conversation. If they're frowning, have their arms crossed, are looking away or tapping their foot, this is usually a sign that they're resistant to the conversation. At this point, you'll need to decide whether to carry on or leave the conversation where it is.
Explore what may work directly with the person, as this will help them to feel more confident of being able to make a change. Wherever possible, encourage the person to identify the best solution themselves, such as:
"What are your thoughts about making a change?"
"What do you think would work for you?"
Be positive and motivational
You should always be encouraging and supportive of any proposed changes, share success stories and encourage the person to talk about the benefits of making a change. It's more motivating for someone to say the benefits themselves, rather than hearing it from someone else, such as:
"What do you feel the benefits will be if you reduce the amount of alcohol you drink?"
"That's great to hear, like you said, being active doesn't have to mean spending hours at the gym, starting to go to a running club or walking with friends are also really good ways of doing more exercise"