Read the message carefully. What is the root of the problem? How can you help?
It's a good idea to document the message. It can be used for training or to share with co-workers who might want to follow up
Remain transparent with your audience. Deleting messages rather than addressing them head-on conveys you might have something to hide.
Timeliness is key here. Most social users expect to see a response within 1 hour. It's necessary to follow up with relevant departments to give customers satisfactory answers.
Draft your response. Remember the basics of good customer service. Your response will be judged not only by the users you're conversing with but by all your followers.
Send your response. If possible, provide an apology and a solution. This is your opportunity to turn a disgruntled customer into a brand evangelist.