Learn Croatian: Spavamo pod novim krovom. - We are sleeping under the new roof.

The preposition pod (under) takes the instrumental case when you are describing a stationary location. Since sleeping is an action happening in one fixed place under the roof, we use the instrumental.

What case would we use if we were running under the roof to get out of the rain?

If there is motion towards a destination, meaning you are moving from outside to underneath the roof, pod takes the accusative case. In that situation, you would say pod novi krov.

Why does the adjective novim end in -im while the noun krovom ends in -om?

In the masculine singular instrumental, adjectives take the ending -im (like novim, dobrim, velikim). Masculine nouns, however, take the ending -om after a hard consonant (like the 'v' in krov) or -em after a soft consonant.

How does the verb spavamo fit with the grammar of the rest of the sentence?

Spavamo (we are sleeping) is an imperfective verb describing an ongoing, continuous action. This perfectly matches the use of the instrumental case for a stationary, unchanging location. A perfective verb indicating a change of state, like zaspati (to fall asleep), would change the feeling of the sentence entirely.