Typika (obednitsa) is a short service that is usually served when a priest is not present; while you can do these in a limited form at home, when they’re in the parish the only stipulation is that the doors on the iconostasis remain closed. A readers’ typika looks a lot like the structure of the Divine Liturgy, minus the priest, and can actually be celebrated by anyone, but should be celebrated by the ranking minor clergy, or if none are available the warden (starosta), etc. on down the line.
A deacon’s typika is a sort of Presanctified Liturgy, a relatively recent innovation based on the ancient practice of deacons taking Holy Communion to homebound folks, and so requires the permission of the bishop. Finally a priest’s typika is used for when the priest would have to serve multiple parishes; since we can’t celebrate more than one Divine Liturgy a day, a typika service would be offered for the others. The typika is a beautiful service and should be the default practice of your family for mornings when you can’t make it to the Divine Liturgy. The text can be found here.