Two scriptures indicating that we must believe on Christ are Acts 16:31 and Romans 10:9. The former says, "So they said, ‘Believe on the Lord Jesus Christ, and you will be saved, you and your household,'” and Romans 10:9 says, "If you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved."
To properly understand these scriptures, we must know what it means to believe. Some people minimize the word believe by defining it as simply knowing Christ exists when it really means trusting Him and living one's life to please Him. Vine's Expository Dictionary of Biblical Words explains that the Greek word pisteuo (the Greek word found in both passages) means "'to believe,' also 'to be persuaded of,' and hence, 'to place confidence in, to trust,' signifies, in this sense of the word, reliance upon, not mere credence."
There is obviously more to receiving salvation than simply knowing Christ lived. While we cannot earn our salvation through good works because salvation is a gift from God (Romans 6:23; Ephesians 2:8-9), God does expect those who come to Him to keep His commandments (John 14:15; Revelation 14:12) and do good works (Ephesians 2:10). Those who truly love God will do these things because they have dedicated their lives to Him (Galatians 2:20).