She used a lot of milk in the cooking.

Literal

She [topic-は] cooking [to-に] milk [object-を] a-lot used.

に marks the destination or target of the ingredient — 'into the cooking.' たくさん ('a lot') is a basic quantity adverb. ミルク is a loanword from English; 牛乳 (ぎゅうにゅう) would be the native equivalent.