The part of the grammar page this lesson drills — read it here, then use it.
У and на - location versus motion
Both у (in/at) and на (on/at) have two different endings depending on the question they answer. For location (где? - where?), masculine and neuter nouns take a fixed -у ending, the same pattern days-months-a1 used for months: у Београду (in Belgrade), на столу (on the table). Feminine -а nouns take -и instead: кућа → у кући (at home).
For motion toward a destination (куда? - to where?), the noun instead takes the accusative pattern from cases-introduction-a1: masculine and neuter nouns stay unchanged, feminine -а nouns become -у. Идем у Београд. (I'm going to Belgrade) leaves Београд unchanged; Идем на плажу. (I'm going to the beach) changes плажа to плажу.
Из, од, до - the from family
Из (out of/from), од (from/since) and до (to/until) all take the same genitive-shaped ending numbers-a1 already introduced as the 5+ count form: masculine/neuter сто → стола-type ending, feminine -а → -е.
Долазим из Београда. (I'm coming from Belgrade), Идем од куће до школе. (I'm going from home to school) - Београда, куће and школе are all genitive-shaped, not nominative.
Special cases
Са (with) takes yet another ending, -ом, on the noun that follows: путујем са сестром (I'm traveling with my sister). The short variant с is used before most words, but са replaces it before words starting with с/з/ш/ж/ц/ч (to avoid an awkward consonant cluster) and always before the pronoun мном (me): са мном, never с мном.
За, in the sense of for - direction or purpose - reuses the accusative pattern from the motion section above; за has other senses with a different case pattern, covered in a later lesson. О (about) reuses the same location endings as у - -у for masculine/neuter, -и for feminine -а nouns: причамо о Београду (we're talking about Belgrade) looks exactly like живим у Београду (I live in Belgrade).