How should children be told that their father is going to marry again?

The father himself should tell them, honestly and in a way suited to their age, after the existing wife has been informed first — children should not hear it from others or from social media.
Every head of a family is a guardian who will be asked about his charge (Sahih al-Bukhari 893), and polygamy is conditional on justice (an-Nisa' 4:3), which children feel too. Things to make clear: his love and responsibility towards them will not lessen; maintenance, time and presence on important days will continue; and they may ask questions or express anger without being punished. Do not ask the children to keep it secret from their mother. Do not ask them to take sides, and the mother too should avoid speaking badly of the father in front of them even when hurt. Teenagers may need a counsellor to process their feelings. See Children in polygamy.