Learn German: Das Kind legt das Spielzeug in den Korb. - The child puts the toy in the basket.

In German, there is no single generic word for 'to put.' You have to specify how the object is being placed. legen is used when you lay something down or place something that doesn't have a distinct 'standing' position, like most toys. If the toy were a standing action figure, you might use stellt (stands upright) instead.

Why is it in den Korb and not in dem Korb?

The preposition in is a 'two-way' preposition. It takes the accusative case when there is an active movement toward a destination (answering 'where to?'). Because the child is moving the toy into the basket, we use the accusative den Korb. If the toy were already resting statically inside the basket, we would use the dative case (in dem Korb or im Korb).

What is the gender of Korb (basket)?

It is masculine (der Korb). We can tell because the phrase in den Korb uses the masculine accusative article den.

Is das Spielzeug in the nominative or accusative case here?

It is in the accusative case because it is the direct object (the thing being picked up and moved). For neuter nouns like Spielzeug, the accusative article (das) looks exactly the same as the nominative article, so you have to rely on context to know it is the object.