A resignation letter can be handed in for a number of reasons. It can reflect on the business if there is a high staff turnover. However, there is always some staff movement as people leave to progress, move abroad or have babies for example. An exit interview is valuable in staff retention by learning where the company can make improvements.
Discuss the letter of resignation with the employee. Receiving a letter of resignation can be disappointing, but it can be helpful to meet with the employee to discuss his reasons for leaving, especially if they are not stated in the letter.
Styling a letter of response depends on the type of company that employs you. Some public companies may have a more standardized style, whereas privately run businesses may work in a less formal way. In that respect the start of the letter may vary from Dear Mr.... or Dear Kevin.
Thank the employee for the letter and tell her you are sorry to see her go. Praise her work briefly and wish her well. You might mention your willingness to give a reference, if it is appropriate.
Writing a response to a resignation letter for some people might be different. If he resigned before he was let go for cause then the letter does have to be formal. In this case thank him for the letter and the work he has done. You can still wish him well but don't need to offer a reference.