What type of psalm is Psalm 78?

Psalm 78 can be classified as a liturgical psalm, a psalm used in public worship.
In relation to its content, Psalm 78 is what's called a maskil, which is a song designed to impart religious teachings. This is done through the medium of history, as the psalm recounts several centuries of Jewish history during which God's chosen people did not respond to his gracious deeds and were punished accordingly.
Two main historical narratives dominate the psalm: the wilderness events and the movement of the Jewish people from Egypt to the land of Canaan. In both cases, a parallel structure can be observed: a gracious act from God is followed by rebellion, which in turn is followed by divine punishment.
The main teaching which the faithful are supposed to derive from Psalm 78 is the overriding importance of having faith in the goodness of God despite the many trials and tribulations to which they are often subjected. The psalm also provides the faithful with a dire warning of what will happen if they should lapse into disobedience.