Grace comes to us when we receive a sacrament. The minister of the sacrament (usually a priest or deacon) performs the sign of the sacrament, and that sign makes happen an action of Christ, which brings us grace. For example, in the sacrament of Baptism, the priest will say “I baptize you in the name of the Father, and of the Son, and of the Holy Spirit” while pouring water three times on the infant’s forehead. These words and the pouring of water makes happen the “washing away” of orignal sin of the infant, which is to say the infant is no longer separated from God. The infant is in a state of grace.
A liturgy is the formal ritual ceremony: the words, actions, movements, responses, etc of the priest and the people, when performing the sacrament. There are liturgies for events that aren’t sacraments too, such as a funeral liturgy, and the liturgy of the hours (which are daily prayers prayed in a certain way).
I hope that helps. Feel free to ask more questions!