By grace alone is the opposite of man's works (Romans 11:6). Those who claim to be working to go to heaven have no understanding about God's grace in salvation. They often say something like this, "Well, we are all working to go to the same place." That place for them is heaven, but they do not know the way. It's by grace alone in Christ alone (John 14:1-6).
By grace alone is the gift of God in Christ our Lord. Grace gives us God's favor as a gift through Jesus Christ. He is full of grace and truth (John 1:16). "For God so loved the world that He gave His only begotten Son" (John 3:16). Jesus is the gift of God. He is the grace of God incarnate.
A gift may be received or rejected. So it is with our Lord Jesus Christ (John 1:11-12). Those who receive Christ are those who believe in Him. To believe is to trust or rely upon Him as our Savior and Lord. There is salvation in no other (Acts 4:12). Therefore, man's works cannot earn salvation, because grace alone makes it the gift of God.
The only work that avails to salvation is the finished work of Jesus Christ. He fulfilled the law of God at every point. He is the only man who ever lived to obey God in all things. His righteousness is imputed or placed on the account of all who believe. We are the righteousness of God in Christ alone (2 Corinthians 5:21). His cross work takes away all our sins (1 John 1:7). Believing on the Lord Jesus Christ receives His finished work for our salvation.
After conversion to Christ, the Holy Spirit works in every believer to produce good works before ordained of God (Ephesians 2:10). These are works of the Spirit, not works of the flesh or man's corrupt nature. God works in us to do His good will (Philippians 2:12-13).
Believers work out what God works in them to the praise of His glorious grace. That's it. Grace works through us. The apostle Paul put it this way: "I labored more abundantly than they all, yet not I, but the grace of God which was with me" (1 Corinthians 15:10). That's by grace alone working through him.