The moment Adam and Eve noticed their shame in Genesis 3:7-8, they covered themselves with leaves and hid from God among the trees. That wasn't the way God intended to cover our shame, but in some form or another many of us use various methods to hide our shame from God and others. We may use rules, doctrines, works or a host of other means, but only Christ will do. Later in Genesis 3:21 God himself sacrificed animals and dressed Adam and Eve in the skins. This action was a foretelling of how God would forgive our sins and cover us with Christ's righteousness.
When we notice our shame, what is the first thought that comes to mind? Do our thoughts settle on our righteous acts? Do we try to convince ourselves of our self-worth? If so we may be hiding from God behind fig leaves. Pure faith in Christ is summed up well by Horatius Bonar, "To get this perfect righteousness all we need to do is agree with God's judgment that we are completely unrighteous, and ask for Jesus to be our representative." The peace of God fills us when we have that kind of faith.