Learn Finnish: Huomaan lentoemännän laittavan turvavyöt kiinni. - I notice that the flight attendant is fastening the seatbelts.

This sentence uses the referative construction, which is a shorter way to replace an että (that) clause. Instead of saying Huomaan, että lentoemäntä laittaa..., the subject of the second action is put into the genitive case (lentoemännän) and the verb is turned into a present participle ending in -van (laittavan).

Why is the subject lentoemäntä in the genitive form lentoemännän?

In the referative construction, the doer of the participle action always takes the genitive case. Since the flight attendant is the one doing the fastening, lentoemäntä becomes lentoemännän.

What is the base verb for laittavan and how does it combine with kiinni?

The base verb is laittaa (to put). By adding the adverb kiinni (closed), the phrase laittaa kiinni means 'to close' or 'to fasten'. To make it fit this construction, the strong stem laitta- gets the -van ending.

What case is the object turvavyöt in, and why?

turvavyöt is in the nominative plural. In a referative construction, the object rules are exactly the same as in a normal sentence. Because the action applies to multiple seatbelts entirely, the plural object takes the standard plural -t ending.