"Kids like jumping."
Translation:Дети любят прыгать.
You can think of the subject as being given enjoyment or pleasure from the object. In this example, детям нравится прыгать, thinking about it as "jumping pleases/brings joy to the children" might help make sense of the cases: since they're being given something, the dative case is used (knowing that давать/дать is "to give" might be useful for remembering that).
I found this bit of information, but I had to fill in accusative and genitive by referring to a declension table. There doesn't seem to be any singular form of Дети, so my source (reverso.net) lists ребёнок as nominative singular. [IOW, дет, Дета, Деть, etc. are not singular forms of Дети]:
Ребёнок - Nom. sing.
Дети - Nom. pl.
Детей - Acc. pl. / Gen. pl.
Детям - Dative pl..
Детыми* - Inst. pl.
Детях - Prep. pl.
The Declensions appear to be from the tables for the ending -ь, which are identical for both masculine and feminine plural in all cases.
*Детыми appears to be an exception to normal declension, which otherwise would be Детями