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When you found your nation, it starts out with 5 million people. For the first few days, your nation's population increases by one million per day: on day two you'll have 6 million, then 7, then 8, then 9, then 10. Eventually your population begins growing faster, as shown below:

Days 1-6: 5, 6, 7, 8, 9, 10 (+1 mil per day)
Days 7-11: 12, 14, 16, 18, 20 (+2 mil per day)
Days 12-15: 23, 26, 29, 32 (+3 mil per day)
Days 16-17: 36, 40 (+4 mil per day)
Days 18-19: 45, 50 (+5 mil per day)
Days 20-21: 56, 62 (+6 mil per day)

Your nation will have 62 million people on its twenty-first day of existence. After that, population growth is randomised, growing from five to seven million people per day. There is no way of changing your population or making it grow faster or slower; issue effects have no impact on population whatsoever. If you simply found your nation and never log into it again, it will cease to exist after four weeks; at this time it will have between 102 and 118 million people (average being 110, and most being within a few million of this). This nation had 112 million people when it was exactly four weeks old.

You can get the issue that allows you to name your capital city at 250 million people, which takes about two months. At 500 million you can choose a custom pretitle (so if you wanted to be "The Fairytastic Unicorn Kingdom of 60s Music", you could; there is no issue that allows this, just check your settings); this takes just over three months. At 750 million (4.5 months) you can get the issue that allows you to name your leader, and at 1 billion (just under six months) you can get the issue that allows you to name your national religion.

If your nation's population is greater than or equal to 1 billion, its name cannot be used by anyone else ever again, not even after your nation has ceased to exist. All you need to do to get your nation's name permanently reserved is use it for about five months; this will be enough to take it over the 1-billion mark before it ceases to exist.

By the end of your first year, your nation will have on average 2.132 billion people, making it one of the bigger nations in the world. Each year beyond that will add an average of 2.190 billion people; on average it takes four years and seven months to reach 10 billion people.

Your nation's population will not increase if it is inactive. If your nation ceases to exist with 385 million people, and you decide to restore it later, it will still have 385 million people, regardless of whether this is the next day, the next year, or ten years later. You will still have the same population, post count, and stats as you had before it ceased to exist. This is why you may occasionally see a nation from, say, 2005 with only seven billion people; it's been inactive most of the time since. Note that you cannot restore a nation that was deleted by a moderator or administrator for rule violations, and no amount of begging, pleading, or threatening will change this.

However, if you create a new nation with the same name as a previous nation, you will not inherit that nation's statistics or population; otherwise this nation would have started out with 260 million people. The owner of the original nation with that name cannot log in anymore as nations are identified by name only.

The nation with the highest population as of this writing is Kyupaa, which has nearly 45 billion people and has been continuously active since its founding in January 2003. (As an aside, when I joined NationStates in 2012 the largest nation had only 20 billion people; now my first nation would have a higher population than that.)

Updated 20190930 as challenge points are no longer restored when a nation is revived.

Updated 20221231 to reflect the increase in population needed for automatic name reservation.