Garbage Can, Garbage Bin, Trash Can, Trash Bin, Waste Can, Waste Bin, Rubbish Bin, Bin
noun
ゴミ means "garbage." Add a box to it and you have a garbage box aka a garbage can or garbage bin.
ごみばこ, ゴミばこ
The reading is just the kun'yomi reading, the one you learned with the kanji. Be sure to pay attention to the rendaku though. はこ changes to ばこ.
ゴミ箱はどこですか？
Where is the trash can?
この部屋にはゴミ箱が必要です。
We need a trash can in this room.
ペットボトルのリサイクルボックスはゴミ箱の横にあります。
The recycling bin for plastic bottles is next to the trash can.