Usage patterns
〈人〉に贈り物をするto give someone a present
I gave my mother a present on Mother's Day.
贈り物を選ぶto choose/pick out a gift
It took a while to pick out a birthday gift for my friend.
贈り物を渡すto hand over/present a gift
I gave her the present at the party.
〈人〉から贈り物をもらうto receive a gift from someone
I received a gift from my teacher.
贈り物を包むto wrap a gift
I wrapped the gift in pretty paper.