Personal hygiene is an incredibly difficult subject to approach, and there's a real risk you will cause offence if you go about it the wrong way. However, there comes a point where you can't ignore the situation any longer. Unfortunately, a lot of people with a personal hygiene problem don't even realise there's an issue – they're often the last to know, while other colleagues are well aware.
If you're going to raise the matter, you need to do so carefully and with great tact. Firstly, make the one-to-one as discreet as possible. If you can, drop it in as an 'aside' to another discussion while you have them alone – for example, 'By the way, while I have you, I've noticed that you might have a slight problem with body odour/bad breath/etc. Please don't be embarrassed about me raising it, but I wouldn't want other colleagues or clients to bring it up.'
Be prepared to defend your comments. People usually feel personally affronted when you raise a hygiene issue, and that's only natural. If you can put it into context, they may feel less 'picked on'. Let them know that this is a purely professional discussion, not a personal one. You could mention that you've noticed some colleagues or clients have requested to work with someone else because of the issue, and you don't want it to impact the business or the individual's own prospects.
You have to handle the matter with such delicacy, but prepare your words in advance, be gentle and they will hopefully take it the right way and act to solve the problem.
Be discreet about the conversation
Drop it in as an 'aside' to another discussion
Back up your comments with examples
Let them know it's professional, not personal