For years, I understood the gospel and salvation in terms of personal belief and faith. I think it would fair to say that this is the course that most evangelical churches have taken, in terms of both understanding salvation as a doctrine and as a message for evangelism. To be sure, it would be unwise to discount the importance of genuinely expressing belief and faith in Christ, as it underscores the necessity of human responsibility in the fruit of salvation.
My understanding of the gospel radically changed, however, when I began thinking of it in the paradigm of spiritual life and conversely spiritual death. We must necessarily view salvation in this context because it puts the reality of sin's stakes in our minds while still giving glory to God for His redemptive work. Trivializing salvation to just a personal decision simply doesn't convey our positional standing before God formerly as sinners but now as new creatures in Christ (2 Corinthians 5:17).
So when we consider the state of human nature, it would be an injustice to simply say that we have sinned and insulted God. Far more accurate is a depiction of utter spiritual deadness-- the fact that all human beings are born into sin, spiritually dead through their federal head in Adam, and have no willful capability to seek or choose God. Genesis 2, Ephesians 2, and Colossians 2 all allude to our death in the spirit and in our trespasses. Just as physical death renders someone incapable of feeling, thinking, moving, etc., spiritual death also incapacitates ability for everything.
To only way to bring about life to a dead person is through resurrection, or something we call regeneration. Simply put, it is the act of restoring life to the dead, an act which must be authored by an external agent, for the dead subject has absolutely no power to regenerate him or herself. One of Scripture's greatest illustrative examples of this is the resurrection of Lazarus. Lazarus did not go about attempting to revive himself, nor did he ask Jesus to resurrect him. Christ simply did it of His own accord, since Lazarus had no ability whatsoever to raise himself from the dead.
In the same way, spiritually dead people are utterly incapable of regenerating themselves. It is an external act of the Holy Spirit that takes place independently of the dead subject's mental, rational, physical, or spiritual faculties. Semi-Pelagian and Arminian theologians will argue that the Holy Spirit will prod someone's heart to believe, but that the individual must ultimately be the one to take the last step (e.g., think the 'open door' analogy). You can almost liken this to the 70-30 dating rule, where the male goes in 70% for the kiss, but the female must accomplish the remaining 30%.
As long as we're talking about dead people here, it's important to remember that the dead cannot move, cannot think, and mostly certainly cannot kiss a wooer back. Not thirty percent. Not ten percent. Not one percent. As a result, a wholly external act of regeneration is credited solely to the one doing the saving. In the context of the salvation of Christ's gospel, we must give glory to God for completely authoring, initiating, and finishing salvation in each believer's life.
All the while, there are still implications for gospel evangelism. Sinners cannot comprehend their spiritual standing before God and, more importantly, their need for a Savior without first understanding their deadness in sin. So when we preach Christ to the lost, it should never be about making a decision as if people can pick and choose whether they need Christ. Instead, it must always be about placing God in His almighty holiness and realizing our utter deadness and spiritual incapacity. Only then can people understand the true need for a Redeemer and Savior named Christ.