"I understand that I am a sinner and deserving of God's Wrath, what must I do to be saved?"
God's Word says He will punish all types and kinds of sin; however, His Word says He forgives all types and kinds of sin. How can He do both?
It is not that God "winks" at sin and forgets about it. God dealt with sin by sending His Son to live a perfect life and die a brutal death on the Cross. God poured His Wrath out on His Son to appease His Wrath, to satisfy the debt of sin. That is how He "punished" all types and kinds of sin - Jesus who knew no sin became sin for us.
That is the Gospel. Jesus said "repent and believe the Gospel". Repent means to have your mind changed regarding the severity of your sin; and the Righteousness of God that must deal with your sin. A mind changed in such a way that you are driven to your knees pleading for God's Mercy and determined to live the rest of your life honoring God, turning away from sin and seeking God's will for your life. You must believe the Truth of the Gospel, that your sin can only be cleansed in the Blood of Jesus, putting your faith, trust, and hope in Him alone to save you from the Wrath to Come.