The psalms redound with this ring to seek the LORD, to seek his face, along with other passages in Scripture. I believe we often do this because we know that we're lost, and that's half the battle.
To seek God's face is to seek his light found in his countenance, revealed to us Spirit-ually, by revelation in an experiential way, not only in the mind. And it is to seek his blessing in helping us through difficulties and impossibilities, to ourselves, that we may walk in the way of the Lord.
What do we do? A good way to go about it is to open up to the psalms. Start at Psalm 1 and begin praying your way through them, in the name of Jesus and even as one in Jesus, that is the psalms impacted and fulfilled by his person and work for us and the world.
This includes confession of our sins and petitions for God's forgiveness and restoration. Of course through Jesus' death we have the forgiveness of our sins, but to receive that we must really want it or choose it regardless of our wants and feelings. And as we seek God we open ourselves up to receive from him his grace to give us what we can never work up in ourselves.
Seeking God is often done in times of desperation, when we know that without God's help we're sunk. But we must be ready and willing to obey, seeking to do so eagerly, from the heart, not sugarcoating any sin, as sweet as it may seem to us, along with the bitterness it brings.
These are just some aspects of seeking God that I see in reading Scripture and in living and trying to do this very thing myself. What have you seen about seeking God?