Questions & Answers about Вчера я подарил сестре новую игрушку.
Why is the word for sister spelled сестре here?
This is the Dative case, which we use for the person receiving something (the indirect object). The dictionary form is сестра, but because feminine nouns ending in -а change to -е in the Dative case, it becomes сестре.
Why are the words for new toy (новую игрушку) spelled with -ую and -у endings?
They are in the Accusative case because the toy is the direct object—the thing actually being given. The dictionary forms are новая and игрушка. In the Accusative case, the feminine noun ending -а changes to -у, and the matching adjective ending -ая changes to -ую.
Does the verb подарил just mean gave?
It specifically means gave as a gift. If you just handed something to someone (like passing a pen), you would use a different verb (дал). Also, because подарил ends in -л, we know the speaker (я) is male. A female speaker would say подарила.
Why doesn't the Russian sentence include a word for my before sister?
In Russian, possessive words like my (моей) are often left out when the context makes it obvious. Since you are doing the giving, Russians naturally assume it is your own sister unless you specify otherwise.