To engage with people, you usually just have to show an interest. Most people love talking about all the details of their lives. Just ask a few questions and then listen. Your brain will begin to process the details and brain fitness will start to increase.
Some of the best skills to practice when dealing with other people (for brain fitness) are to try to understand the other people's state of mind, try to understand complex personal problems involving more than one person and trying to focus on the important details. Remember, as with any brain fitness activity, the key is to stay engaged and interested. You should be genuinely curious about learning everything you can from your relationships.
Must Read: Relationships and Health