Learn German: Der Großvater spielt mit dem Kind. - The grandfather is playing with the child.

The preposition mit (with) is a dative preposition, meaning it always forces the noun that follows it into the dative case. Because Kind is a neuter noun (das Kind), the word for "the" changes from das to dem.

The translation says "is playing". Why isn't there a translation for the word "is"?

German doesn't have a continuous tense like English does (using "is" + an "-ing" verb). The single verb spielt translates to both "plays" (in general) and "is playing" (right now). You just rely on context to know which one makes sense.

If he were playing with multiple children, how would the sentence change?

It would become Der Großvater spielt mit den Kindern. In the dative case for plural nouns, the word for "the" becomes den, and you usually have to add an extra -n to the noun itself. So the standard plural Kinder becomes Kindern.

Can I change the word order if I want to emphasize the child?

Yes! You can move the phrase about the child to the very beginning: Mit dem Kind spielt der Großvater. Just remember the golden rule of German main clauses: the verb (spielt) must stay in the second position, which pushes the subject (der Großvater) to the other side of the verb.