I can't speak for the population of the earth as a whole, though estimates would certainly be possible. Maybe not entirely accurate, but that doesn't matter too much for most cases. The populations of North America or Australia don't matter when looking the medieval Far East.

However I can speak for part of the world. In China, a census was taken regularly throughout various periods of time. For example under the Ming, they were done every ten years. Like the census today, that wasn't without problems as not everyone wanted to be counted. If you're family is accurately counted, your taxes will be higher than if you can keep a couple people off the census. That said, there are some notable exceptions which saw people wanting to be taxed as part of a push for urban reform.

During other periods of Chinese history, the census wasn't necessarily as frequent as under the Ming, but it still happened. There recorded official number for the Song was about 50 million, though there's reason to believe that was on the low end of the dynasty's population range from start to finish. The Tang census has the number of households about the same, but again there are estimates that the number increased significantly after the counts were made.

Why all these estimates? Accurate numbers were hard to get. Even today, the exact population of modern China is unknown, and the official numbers are almost certainly not accurate for a number of reasons. It's for this reason that estimates are still made. But, fortunately, they're not pulled from thin air; we do have written records to go on.

Likewise, Korean dynasties have generally undertaken nation-wide census counts, going back quite a ways. It's these kinds of documents, as well as estimates based on additional sources (such as reports by invading armies/conquering nations etc), that give us an idea of the populations for various regions. Put them all together and you can start to have an idea of what the world population might have been.