I asked the same question basically on another board the other day. Here is the response.
I think this is the standard understanding with regard to your questions, but first the Scriptures: 2 Cor 5:6, 8:
Therefore we are always confident, knowing that, whilst we are at home in the body, we are absent from the Lord. . . We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord.
And then there is Paul (again) talking of whether it is better for him to remain in the body or to go to be with the Lord, in Phil 1:23, 24:
For I am in a strait betwixt two, having a desire to depart, and to be with Christ; which is far better: Nevertheless to abide in the flesh is more needful for you.
In Hebrews Paul also describes Heaven—what is called the "intermediate state" (where the saints go before the judgment day, and our eternal lives after the great resurrection on New Earth) :
But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect, And to Jesus the mediator of the new covenant...
So, to briefly answer you: When a believer in Christ dies he or she goes to be with Christ and the other spirits of just men and women made perfect in Heaven, where they await the general resurrection; after that is over, they go to their final destination, which is briefly described here, in Rev 21:1-4:
And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea. And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God. And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.
This is the final place for the children of God, to be on New Earth with their Saviour and God, where we shall enjoy the great marriage supper of the Lamb, Rev 19:7-9:
Let us be glad and rejoice, and give honour to him: for the marriage of the Lamb is come, and his wife hath made herself ready. And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen is the righteousness of saints. And he saith unto me, Write, Blessed are they which are called unto the marriage supper of the Lamb.
Anthony Hoekema wrote an interesting piece on life on New Earth, Heaven: Not just an eternal day off (excerpted from his book, The Bible and the Future). I hope this answers your questions