Romans 8:28 - 30
ESV - 28 And we know that for those who love God all things work together for good, for those who are called according to his purpose. 29 For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
The only part we play in salvation is committing the sin that necessitates an attonement.
Salvation is deliverance. As such, we play the part of the person needing rescue (fallen humanity). We also play the part of recognizing the need for rescue (acknowledging our sin), and accepting rescue (faith) rather than rejecting it. This does not mean that we in any way 'accomplish' part of the salvation/deliverance itself.
God set the plan of salvation up in such a way that we do need to do 'the work that God requires' and believe in Jesus Christ. (John 6:28-29)
Only those who believe in Jesus will receive eternal life (John 1:25, John 3:16)