Baptism is an important ingredient here, too, but for the moment let's look at repentance and forgiveness.
Many Christian traditions, and many individual Christians, choose to focus on one or the other of these. Some people are repentance-focused: "I'm so bad. I did wrong. Please forgive me, Jesus. I failed. I am a sinner." There is a hopelessness to this expression. There's little if any joy involved. This "faith" is more like chronic depression.
Other people jump right to forgiveness without doing any repenting. "I'm free! I'm victorious! I'm joyful! Jesus loves me and he wants me to be happy!" There's a joy not only without sorrow but without seriousness, like a perpetual sugar high.
When Jesus calls people to follow him, he calls us to both repentance and forgiveness. In fact, repentance becomes the entrance to the Christian experience, and forgiveness becomes the experience of unimpeded fellowship with God.
So what is repentance? In Greek the word is metanoia, and it literally means to turn around. So what we described earlier as repentance -- feeling bad, emotionally beating one's self up -- is not really repentance at all, because it doesn't involve any turning. Repentance recognizes my error, and then turns away from it. When I recognize the place I have fallen short, I bring that sin to the foot of Jesus' cross in prayer. In that encounter with Jesus I receive a clear word of forgiveness, a costly forgiveness that buys my freedom at the price of Jesus' blood. At times I am tempted, because forgiveness is so costly, to want to cling to my sins, not to burden God with them. But this is foolish, for even the smallest sins are a burden too great for me to bear. And the love of Jesus that put him on the cross is limitless. So his desire for me, and the best thing for me to do, is to go freely and often to the cross in repentance, confessing my shortcomings, laying my faults at the foot of the cross, and as best I can turning from those faults and surrendering to Jesus, asking God to change me when I cannot change myself.
When I rise up from the cross, I turn to the risen Jesus, victorious over death and hell, who gives me the free gift of forgiveness, life and salvation. Because, as Luther said, where there is forgiveness of sins, there is also life and salvation. Coming in humility to the cross opens to me the life that Jesus longs to give me. This is why he paid the price of giving his life -- not so I can squeak into heaven, hanging my head at the entrance and hoping to just get through the closing doors -- but so that I can come to him in confidence, knowing his love, and freely receiving from him the greatest gift I can imagine, the gift he longs to give more than anything.
It is this new life God longs to pour into our hearts by his Spirit, but our sin prevents us from receiving. We are like empty corked bottles longing to be filled. Our sin is the cork that needs to be removed by the corkscrew of the cross so that God's Spirit can be poured into us. And the trouble with us is, we keep re-corking ourselves! This is why repentance is not a one-time event but a returning, morning after morning, day after day, to the cross. And repeatedly we rise up forgiven, renewed, enlivened.
You can't have new life (forgiveness) without repentance; you can't live in real repentance for any length of time without rising up renewed. They're like two sides of a coin that rotates through our lives.