That is a fair question and a good one, that Matt asks. You can read all of this, or you can jump down to where I answer the question directly rather than explain why, in some ways, it is harder than it looks.
There are some problems. That is why the problem is harder than it looks
Some people refuse to be comforted. They just aren't ready.
Some people refuse to accept that what comforts them does not comfort others.
Much of what passes for "comfort" is actually the speaker explaining why what every causes you to need comfort will not afflict them, or making your problem right or solved in their mind.
To give comfort ....
First decide if someone needs friendship, companionship, counseling, advice, witness/confirmation, guidance or comfort. Those are different things. For example, we had a dear sister in a ward I was in who had some mental problems. In addition to medication, she needed to regularize her sleep and get mild aerobic exercise. A member of her ward by the name of Sister Davis got up every morning and walked with her.
She did not offer advice or guidance. It wasn't friendship or counseling. It wasn't comfort. But with companionship the other sister was able to get up early (which meant she went to bed early and regularized her sleeping) and walk (which meant she got the exercise she needed).
In law school I felt like I should volunteer to help a friend's booth at some activity on the main campus. So, I manned the booth for several hours. Ended up talking with someone whose mother had committed suicide. What they needed was the spiritual witness that she had died as the result of illness (which she had) and was not damned. Which is what the Spirit testified to her (and, observing, I learned a lot about the subject I had not known about). That was not counseling (she had had that) and it wasn't really guidance or comfort. It was witness/confirmation of the Spirit.
Some times that helps. But sometimes the force of the pain or grief is just too much.
So, what can you do to comfort, when other things are not right, do not help or there is too much pain for them to work?
First, realize that when you have a large congregation, some will need friendship, companionship, counseling, advice, witness/confirmation, guidance or comfort -- maybe all, maybe none. Preaching a sermon on repentance (which is an essential part of the gospel) will help some and not others. It may even give comfort.
The same is true of sermons on standards. Some times it gave me comfort to hear someone talk about the value of standards I upheld and what was what I really needed. Sometimes it just bored me. Even the same person can be someone with different needs at different times.
Second, your audience needs to accept that they are not the only audience, at least when they are part of a congregation.
Given that, how do you provide comfort, one on one?
- Comfort the other person, not yourself.
- Listen before you talk.
- Express sympathy, admit that you do not know what to say. "I'm so sorry, I don't know what to say" is not a bad start. "Tell me about it." is a good follow-up.
- Avoid advice unless asked or unless you have professional grade ability or better. Most advice or explanations are really just comforting yourself, not the person who needs it.
- Realize that while it makes you feel good to offer support or commitment to future acts, you probably will not really follow-through on anything. Don't make offers you can't keep. (I still remember some offers from people, and when all I needed was an e-mail returned, they were too busy).
- Do not use the phrase "you don't need anything do you?" or anything like it.
- If you talk about God's love, avoid turning it into a circular platitude (God loves you, so you don't really need comfort from anyone else).
If you really intend more, then " let me know you don’t forget about me the instant I’m out of your line of sight. The physical, practical challenges of life I can handle by gritting my teeth and pressing on; it’s the aloneness that I can’t cure on my own" -- that comment captures it very well.
If you are in a group setting (such as speaking from the pulpit), much of comforting comes from the image of Christ as the man of sorrows, acquainted with grief.
But, before you try to comfort someone, decide if you are really willing to comfort them or if you just want to comfort yourself.