Many times when a person is stuttering it is due to tension in their speech mechanism. So the best response to a person who stutters is to act completely natural, relaxed and take an interest in what the person is saying. This will help the person who is stuttering to relax and help them speak more easily. Its not advisable to 'pull a face' when the person is in a block, avoid eye contact or complete words for the person. This will only further increase the tension and make the person's speech less fluent.
What you can do is say something short and encouraging like:
No stress, take as much time as you need.
OR
Your speech doesn't bother me at all, I really like talking to you.
Don't try and give helpful advise like
Just take a deep breath, think carefully what you want to say and then speak.
as your intentions may be good however it will only add more pressure to the person and lead to further blocks.
I know that I have been in some extremely tight blocks and an encouraging word from someone has just helped ease the situation and improve my fluency.
An important comment here is that stuttering is not always due to tension. The person may be relaxed, free of anxiety and still stutter. For example I may be in a situation where I am completely relaxed but still stutter (for whatever reason) on words, eg speaking to a close friend.
