Charles Spurgeon wrote, "My faith rests not upon what I am or shall be or feel or know, but in what Christ is, in what he has done, and in what he is now doing for me. Hallelujah!" That's your faith resting in Christ alone.
Faith in Christ alone means you do not trust in self-righteousness (Titus 3:4-5). Faith is resting in the righteousness of Christ (2 Corinthians 5:21). He is your righteousness. Believers are accounted to be the righteousness of God in Christ.
Spurgeon's faith was "in what Christ is, in what He has done, and in what He is now doing." That's faith in Christ alone. He alone is your confidence and assurance of salvation. We rest in Christ alone as our Surety (Hebrews 7:22). Faith in Christ is your guarantee of eternal salvation. Christ alone is the assurance of your salvation. There is salvation in no other (Acts 4:12).
Faith in Christ is through the gospel. Confess, "I am a sinner for whom Christ died." Focus your faith upon Christ crucified for your sins and risen from the dead (Romans 10:9). No self-righteousness do you claim. Believe that Christ died for all your sins. Believe that Christ is risen from the dead as your living Lord. That's your faith in Christ alone.