A considerable number of Ukrainian nouns have stable or predictable stress, and are therefore easy to learn. Once you know where the stress falls on the dictionary form of, for example, газе́та - newspaper, кімна́та - room, пи́во - beer, буди́нок - building, you don’t need to worry, as it stays in the same place in all the cases in both singular and plural. There are two types of noun like this: those with stable stress on the stem (examples above); and with stable stress on the ending, e.g. пора́ - season, стаття́ - article, тепло́ - warmth.
Not all nouns, though, have stable stress. There are two distinct types of noun with shifting stress: those with stem stress in singular, shifting to the ending in the plural, e.g. жі́нка / жінки́ - woman, го́лос / голоси́ - voice, мі́сце / місця́ place; and with end stress in the singular, shifting to the stem in plural, e.g. війна́ / ві́йни - war, село́ / се́ла - village. And, inevitably, there are some nouns whose declensions have variations on the above.
To help learners of Ukrainian, and particularly beginners, acquire correct stress, examples of the four types of noun are given below (click on the links), together with frequently-used nouns of the various types and exercises. The principal rules are also given, for those interested in how the language works. For a theoretical analysis of the stress issues, and an attempt at generalising the processes underlying inflectional stress in Ukrainian nouns, see Butska, L., Faithful Stress in Paradigms: Nominal Inflection in Ukrainian and Russian, Rutgers University, 2002.