This is an important construction based on the Aidiacht Shealbhach and the Ainm Briathartha

The Ainm Briathartha is the form of the verb after ag: ag cur; ag moladh; ag déanamh etc
The Aidiachtaí Sealbhacha Possessive Adjectives are as follows: mo (my), do (your), a (his), a (her), ár (our), bhur (your, pl.), and a (their). They behave differently with nouns beginning with consonants from nouns beginning with vowels

(An earlier lesson introduced the possessive adjective - aidiacht shealbhach)

While one can write ag moladh na mbuachaillí one must not say ag moladh iad. Instead write á moladh i.e. ag + a their + moladh at their praising. Here is a list of other examples of this construction first with verbal nouns beginning with consonants and then with vowels.