Each time I have left a position, I have left a little 3 ring "bible". The front page is a list of my job tasks and the rest of the pages are how I do those tasks. If I had already trained someone in on the tasks, I just put basics and write to ask the new person for directions. I have been thanked repeatedly for these.
My supervisor of many years left her position as Head of Youth Services a couple of years ago to take a job as director of a distant library. She had been in our library for over 10 years. She requested that we make a memory book for her to take with her, which we decided to turn into a drop-in craft for our patrons. We set up a shelf in the Youth Services Department with scrapbook pages, ribbon, stickers, markers, etc., and posted a sign explaining that she was leaving, and inviting people to make pages for her book. Over the next few weeks, as news of her departure spread, people we hadn't seen in years dropped in to make pages, as well as all of our current "regulars." Some brought copies of pictures they had taken in past programs, or school pictures of themselves. We also had the digital camera out, and took a lot of pictures as people came in. Right before she left, we assembled all of the pages in a book and gave it to her in a gift box. We also contacted the moms from her very first preschool storytime group (as many as we could find) and asked that they bring their kids in for a group photo. Six or seven of them did. Their kids were all in high school by then, and most of them quite a bit taller than my supervisor! We also took a picture of her with her current group of 2-year-olds, then framed both photos and gave those to her. When she got to her new job, they went on the wall in her office. Needless to say, she was quite pleased with the whole effort, and it turned out to be a good way to help the community to say good-bye to her.
I have found when you are leaving and someone else is taking your place, it helps if you can introduce them at storytime or a regular program like a TAB meeting, etc. If you introduce your replacement and endorse them, it helps the kids to know that they are not just a stranger, but a friend of a friend.