The part of the grammar page this lesson drills — read it here, then use it.
Days of the week
The seven days: понедељак (Monday), уторак (Tuesday), среда (Wednesday), четвртак (Thursday), петак (Friday), субота (Saturday), недеља (Sunday). Four are masculine consonant-ending nouns (понедељак, уторак, четвртак, петак); three end in -а and are feminine (среда, субота, недеља).
To say on a day, use у + accusative: masculine days don't change (у понедељак), feminine days take -у, just like the feminine nouns in cases-introduction-a1 - среда → среду, субота → суботу, недеља → недељу.
Months
The twelve months: јануар, фебруар, март, април, мај, јун, јул, август, септембар, октобар, новембар, децембар - all masculine, and all international/Latinate names.
To say in a month, use у + a special -у ending: у јануару, у марту, у септембру. This ending belongs to the locative case (covered fully in a later lesson) - for now, just learn у + [месец]у as one fixed chunk.
Special cases
Недеља means both Sunday and week - context tells them apart. A less common synonym, седмица, exists specifically for week.
The one exception is positional, not lexical: a day or month name is capitalized only when it happens to start a sentence, exactly like any other word - never in a date or a title.