Learn German: Die Wäsche liegt noch in der Küche. - The laundry is still lying in the kitchen.

The preposition in is a two-way preposition. Because the laundry is already resting there (answering the question where? or wo?), it takes the dative case. The dative form of the feminine noun die Küche is der Küche. If someone were actively carrying the laundry into the kitchen, it would describe a change of location and take the accusative case (in die Küche).

Why do we use liegt here instead of steht or ist?

In German, objects are usually described by their physical orientation rather than just saying they are somewhere. Because a pile of laundry is shapeless and rests flat on a surface, it lies (liegt). If it were an upright object with a base, like a fridge, you would use steht (stands).

Is die Wäsche singular or plural here?

It is singular. Just like the English word laundry, die Wäsche is a collective noun treated as a single item. You can tell because the verb is conjugated in the third-person singular form (liegt), rather than the plural form (liegen).

What role does noch play in this sentence?