When the noun is plural but the number isn't specified, when do you use nominative and when do you use genitive?
With скі́льки 'how much', you put the noun in genitive. The same is true for бага́то 'many, much', ма́ло 'few, little'. (Note this is true for both singular and plural nouns: скі́льки кана́лів 'how many channels?', скі́льки води́ 'how much water?' — both кана́лі and води́ are in genitive case.)
In other cases, you look at the meaning of the word and grammar of the sentence to determine the case. In general, the case for plural nouns is the same as for singular nouns. E.g. if singular is in instrumental case (Я задово́лена цим кана́лом 'I'm pleased with this channel'), then the plural would use instrumental too (Я задово́лена ци́ми кана́лами 'I'm pleased with these channels').
A plural noun can be in any case, just like a singular.