We accept Christ—His birth, life, death and resurrection—by recognizing and accepting His divinity. He is “God with us” (Matthew 1:23), whose mission on earth is to save us from our sins, so we surrender to Him as Savior; and that surrender also makes Him our Lord.
It is an act of faith to invite Him, by prayer, to reside in our hearts/minds as Savior and Lord. We allow Him through His Word, and through the influence of His Holy Spirit on our spirit, to forge a reconciliation between Him who is holy and us who are sinful. The reconciliation is a process, not a one-time event.
The proof that we have accepted Him is the change we, and others, see in our character. Our sinful nature no longer controls us. All the bad habits which His commandments disallow—idolatry, blasphemy, lying, stealing, adultery, coveting, hate and everything else sinful—become distasteful to us.
Under the influence of His Holy Spirit, we begin to strive for a principled life powered by: love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, self-control (Galatians 5: 22,23).
Everything about us—thoughts, attitudes, speech, deportment, conduct in relationships, media choices, self-care, care for others—show spiritual growth. That evident, continuing maturity is the proof that we are Christians.