I've seen неделю, but I don't know of when the transformation occurs. Could somebody explain it to me?
Неделю is the accusative singular. The ending comes from a Proto-Slavic nasal — *neděljǫ — which is a cognate of the accusative ending -am of the Latin first declension, e. g. agricolam vidi "I saw a farmer [agricola]". The ancient Slavs kind of Frenchified that [am] to a twangy [oⁿ], which then lost its twang and became a clear [u] in Russian.
And that Latin example shows you the basic usage of accusative: it's the direct object case. E. g. Вот как я провёл эту неделю "That's how I've spent this week."
The accusative is also the case used with certain prepositions; the logic of which prepositions take which cases is old and often unclear, so no examples, to keep this simple. You'll come to that eventually.
Finally, since неделя is a word for a period of time, its accusative has another important usage — it means "for [the duration of] a week". Just like минуту can mean "for a minute", and год means "year" but can also mean "for a year" (since its accusative happens to have the same form as its nominative.)