A lot depends on the circumstances and what kind of character the neighbour is.
In most circumstances, asking a few questions, listening and drawing them about to talk about it at in greater depth works well. Just listening is often enough on its own.
Best never to give advice unless they've specifically asked for it and you're an expert in that field.
Counselling takes advanced skills. Usually, how a person feels is a natural response to a situation given their conditioning. When that's the case, validating their reality is helpful.
Sometimes they've got their interpretation in a twist and the situation may need to be re-framed.
Anxiety is a special case. It requires asking how real is the risK/ what's the worst that can happen? What is within my power to avoid, reduce or mitigate the risk? What are my options? Anger is a special case. Grief is a special case. Manipulative inverse-narcissists and moochers are a special case. The list of specials goes on and on. It's mostly about asking the right questions so that a person finds their own solutions.
There are free telephone counselling services such as the Good Samaritans.
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