Where your confusion seems to lie is in the fact that salvation (forgiveness) is a gift from God. This is what Christians believe.
Jesus died on the Cross so that our sins might be forgiven:
Matthew 20:28 KJV
Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many.
The reason for this is rather simple: salvation is a gift from God due to his enormous grace.
God sacrificed his son on the cross so that we might receive his gift of salvation, but just as any other gift it must be received by the person to whom it is presented.
For instance if you never open your Christmas gifts, they are still gifts, but they do not do you any good until you do open them and begin to use them. And if you never do it is not the fault of the person who gave the gift.
So it is with salvation. It is there just waiting -- for acceptance, and even beyond acceptance -- to be used by the receiver. The two go hand in hand.
When Jesus died on the cross, God heaped on him punishment for all the sins of the World, but it must be remembered that as terrible as it sounds that too was a gift (albeit a miserable gift), and as with all gifts Jesus had to accept them.
Colossians 2:13 KJV
And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
We must also remember that a gift not only has to be received, but it must also be given. And remember that those are our sins, they do not belong to either God or Jesus, therefore it is we who must make a gift of them to Jesus so that he too can make use of them to justify his dying on the cross. Since he has to take the punishment, we should at least make it worth his sacrifice.
The next step would logically be to do that, but the question is how can we?
Well that's a good question and I'm glad you asked it!
1st John 1:9 KJV
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
Here is how it is done:
We must admit that those sins belong to us. (that is confession)
We must ask God to allow Jesus' death on the cross to be the remission of our sins (ask for forgiveness).
God will then turn to Jesus (who is at his right hand) and ask if he will accept your sin. (Of course Jesus will say yes since he already suffered torture in your name.)
At that time your sins will be taken from you and sacrificed on the cross with Jesus. That is forgiveness.
Believe then that your sins have been paid for in full, and you have been born again, not of the flesh but of the Spirit, and you have become worthy to enter Heaven since you are now sinless in God's eyes, and have become perfect as Jesus was perfect.
The key word here is believe.
1st John 1:12 KJV
But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
As I said before a gift is only a gift not only when it is opened, but it must also be used.
Suppose you are given a car, and all you do with it is set it up and look at it.
It is still a gift and it is yours but until you start to drive it you are not making use of your gift.
There are two ways in which you can use your gift of Salvation, you can bask in it, which God wants you to do.
John 10:10 KJV
The thief cometh not, but for to steal, and to kill, and to destroy: I am come that they might have life, and that they might have it more abundantly.
I like the "more abundantly" part!
And you can also share it. (Which is what I am doing now.)
Here are some other Scriptures which help to explain.
Mark 4:12 KJV
That seeing they may see, and not perceive; and hearing they may hear, and not understand; lest at any time they should be converted, and their sins should be forgiven them.
Matthew 9:6 KJV
But that ye may know that the Son of man hath power on earth to forgive sins, (then saith he to the sick of the palsy,) Arise, take up thy bed, and go unto thine house.
Ephesians 4:32 KJV
And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you.