If you survey John's Gospel, I think the biblical data appropriately defines the necessary grounds for "belief" in John as believing in Jesus Christ as the Messiah, Lamb of God, Son of God, Son of Man, I AM, and the Logos. Throughout John, the theme of believing occurs approximately ninety-three times, clearly indicating an important motif due to its repetitive nature. Yet, the repetitive nature is not autonomous, but always is in conjunction to psychosomatic unity [i.e. heart and mind] of knowing the true identity of Jesus Christ that is followed up with transforming faith and obedience. Therefore, to belief in this new way is a summation to essentially encounter-experience-follow-and-obey the Lord Jesus Christ.
To understand "belief" in John, the key is to follow the literary structure. Viewing the beginning of John as a stage presenting the first act of a threefold story about believing in Jesus Christ is the critical, followed by a second act and finale (i.e. Introduction [who is Jesus], Body [events revealing who is Jesus], Conclusion [purpose to know who is Jesus]).
John 1:1-51, the introduction reveals the emphasis of belief in John.
John 2:1-20:29, the body explains the dynamism of belief in John.
John 20:30-21:25, the conclusion reveals the purpose of belief in John.
Most scholars believe it is possible to develop all of the themes in John solely out of the first chapter alone, and it is not surprising that the "belief" motif starts in that section.
Beginning in the first chapter of John, we see the genesis of the "belief motif" in John 1:7, "He came as a witness, to bear witness about the light, that all might believe through him." Structurally placed between the first usage of believe and the beginning of prologue and first pericope (v.1:1-51), John records the identity of the light as Jesus Christ (vv. 1:4, 5, 8, 9), and affirms the progressive evangelistic nature of believing in Jesus Christ through the witnesses who testified and followed him (vv. 1:37, 40, 43). The first chapter ends with Jesus asking if those following him believe in John 1:50, "Jesus answered him, “Because I said to you, ‘I saw you under the fig tree,’ do you believe? You will see greater things than these.” The concluding statement issues an important question that is presented to all of the characters throughout the rest of the gospel, "Do you believe?" The evangelist begins his gospel by introducing a thematic emphasis for his letter, "Do you believe in Jesus Christ? If not, read about the Son of God in the next few chapters, and I will ask you this question again at the end of my gospel to see if you believe" [italics are mine].
After the introduction, the body of the gospel consists of Jesus explaining the dynamism of "belief" and why someone must believe in him (vv.2:1-20:29). Notice the last verse concluding the life, ministry, death, and resurrection of the Son of God in John 20:29, "Jesus said to him, 'Have you believed because you have seen me? Blessed are those who have not seen and yet have believed.'” John wraps up the story with a defining statement by Jesus Christ. John returns to the "belief motif" to set up his conclusion and purpose.
The conclusion of the gospel ends with a purpose statement and unique event which points back to the emphasis of the statement (vv. 20:30-21:25). The conclusion of the gospel reveals the purpose and reason for the emphasis of "belief" in John 20:30-31,
"Now Jesus did many other signs in the presence of the disciples, which are not written in this book; but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name."This purpose statement concludes the reason why John wrote his gospel, "That by believing you may have life in his name" [italics are mine]. As John begins his gospel with the "belief motif" he concludes with it. Following the purpose statement is a unique event that confirms Jesus as the resurrected Lord and God. In these short resurrection appearances, the"belief motif" is only enhanced by more evidence to convince the reader to believe in the Messiah Jesus.
John does a great job of explaining throughout his gospel what it means to believe in a dynamic way. The Jews believed, but they did not believe God's Word correctly. The Greeks believed, but they did not believe in God correctly. Believing in something that is truth and corresponds to reality is the key in John's gospel because Jesus proves he is the truth over and over again with salivific implications. Therefore, when we tell people to believe in Jesus Christ, we must teach what it really means to believe in him by sharing the entire gospel message!