The first and most important thing is for them to realize that it is a blessing and not a curse. Like any gift a person has, such as writing, dancing, or playing music, it's important to get an understanding of the gift and grow into it over time. Take things slowly. (Resist bombarding them with books, movies and TV shows about the psychic world. And please don't push them into psychic fairs to do readings. While these might come from a loving heart for them, these can create an overwhelming pressure of expectation on them, which can lead to deeper problems.)
An important thing for a child showing abilities is to have a journal and pencil, so that they can write down impressions and experiences. This will help them to learn how their own unique gifts work, as well as discover the unique way they experience the world.
Boundaries are also important. Just as having boundaries in the physical world are helpful, it is also important in the psychic/spiritual world as well. Letting them know that when they say no, to mean no; this is vital. They do have a degree of control, and it's important for them to learn how to use that control, rather than succumb to the notion they are victims.
Children with abilities can sometimes have difficulty sleeping at night, so soft background music can help to soothe and distract their conscious mind so they can sleep more easily.
Most importantly, they should know that they are not alone, and that it is good to embrace the gifts they have. Letting them know that they can be who they are, and that you will be there to love and support them is the most beautiful and loving thing you can do.