The LDS conception of the afterlife is actually more complicated than many realize. I think this would be a good place for a basic primer on what we call the Plan of Salvation:
As already discussed, we started off as spirits without bodies, in what is sometimes called the 'Premortal Life'. Because suffering and pain, as well as the ability to make our own choices freely, were necessary for our further growth, a plan was developed wherein we would go to earth, be given bodies, and be allowed to make our own moral choices, with the knowledge that we would be judged on them. Since, however, it was inevitable that we would sin, and no sinful thing can withstand the presence of God, it was vital that a Saviour be provided who could pay the price of sin for those who accepted it, and thus they could be free from their sins. So we received a body and came to earth. Here, some learn of this plan, and those who know it try to share it with others, but we all have a conscience and some sense of morality, which we need to obey as best as we can. After we die, there will be a period in which all will learn of this plan, and be given the chance to accept Christ, or reject Him freely if they wish.
Then we will be judged and sent to one of what we call 3 kingdoms or degrees of glory: the Celestial, where those who are worthy of the presence of God will live, and may continue progressing to become gods some day; the Terrestrial, for those who were less faithful in following Christ; and the Telestial, for those who led sinful lives and did not repent. The twist to all this is that even the lowest, to which the truly evil will be condemned, is a better and more joyful state than any which can exist on earth. However, those sent there will have an eternity to spend with the memory of their sins. So, for example, Hitler will spend forever to contemplate on the meaning of having millions of people murdered. Likewise, those who have strived for righteousness will be able to live in the presence of God.
A former president of the church once specifically said that atheists (as well as Muslims, Buddhists, etc.) would be able to reach the highest levels of the Celestial Kingdom, if they accepted the Gospel in the next life. However, the reason we try to share it with people now is that knowing this plan makes it easier to follow, and we will know what it is that we have to do to reach it.