finally ~; at last ~; in the end
ついに marks that something has happened after a long wait or effort, often with a sense of relief or significance.
ついに means 'finally' or 'at last', and it is used when something that was expected, awaited, or worked toward for a long time actually happens. It often carries emotional weight, such as relief, excitement, or a sense of an ending. For example, after years of saving, you might say you finally bought a house. It is commonly used with the past tense to talk about completed events, but it can also be used with the present tense to show that something has just now occurred, or with negative forms to mean 'never' (as in 'in the end, it didn't happen'). However, the negative use is more advanced; at N3, focus on the positive sense of 'finally'.
ついに is an adverb, so it does not conjugate. You place it in the sentence, usually right before the verb or predicate it emphasizes, but it can also appear at the beginning or after the topic for emphasis. It is neutral in formality and appears in both speaking and writing, though in casual conversation it is very common. It is not particularly formal or literary.