A couple passages that I always turn to that represents the theme throughout scripture are John 3:16-18, and Ephesians 2:4-9:
For God so loved the world, that he gave his only Son, that whoever
believes in him should not perish but have eternal life. For God did
not send his Son into the world to condemn the world, but in order
that the world might be saved through him. Whoever believes in him is
not condemned, but whoever does not believe is condemned already,
because he has not believed in the name of the only Son of God. ~ John
God has "elected" that anyone who believes in His Son, Jesus, and follows Him will be saved. Contrariwise, He has "elected" those who reject His son to eternal death in hell.
But God, being rich in mercy, because of the great love with which he
loved us, 5even when we were dead in our trespasses, made us alive
together with Christ— by grace you have been saved— and raised us up
with him and seated us with him in the heavenly places in Christ
Jesus, so that in the coming ages he might show the immeasurable
riches of his grace in kindness toward us in Christ Jesus. For by
grace you have been saved through faith. And this is not your own
doing; it is the gift of God, not a result of works, so that no one
may boast. ~ Ephesians 2:4-9
Note the boldened portion (v. 8-9). We are saved by grace, through faith, not works.
I realize these are only 2 passages, but I assure that these represent a consistent theme throughout scripture in that God offers salvation to all, and that all who accept this gift (via belief in His son, having faith in Jesus alone) will live in heaven. Nothing you can do can save you (Ephesians 2:9), therefore it is faith in Christ alone that saves you.
That said, some may say the fact that you place your faith in Christ is an action you make, or in other words, placing your faith in Christ is a "work." But this is misunderstood, because it is like receiving a gift from a a loved one. They offer the gift, and you have the choice to accept or deny it. Likewise, God initiated the relationship by offering us the gift of salvation, and we have the choice to accept it through faith in His Son or deny it through rejection of His Son.