That's an interesting question, Sarah. According to Savory in "Naming the
Living World" (p. 108), Linnaeus named about 6000 species, a record number
for any individual. This sounds like an impossible task, but it's not.
Let's take a look at how he did it.
 
Linnaeus published the first edition of the Systema Naturae in 1735 at the
age of 28. It was a booklet of 11 folio pages (folio pages are large,
though). He kept revising it and it kept selling out, running through 16
editions in his lifetime. But he didn't use the binominal (genus + species)
system consistently until 1753 in his Species Plantarum (1st edition), and
1758 in the Systema Naturae (10th edition). So 1753 is accepted as the
starting date for most kinds of plant taxa (genera, species, etc.), and
1758 is the starting date for animal taxa. Earlier names are ignored.
Anyway, the books kept getting longer with each edition, but at no point
was Linnaeus faced with an impossibly huge task, just a very large and
difficult one. He acquired specimens of many of his species by trade,
purchase, and collecting, and most of these type specimens are still
preserved in a vault in England by the Linnean Society, which bought them.
But he did not have to acquire specimens of everything; in many cases,
Linnaeus simply referred to an earlier published work to document their
existence; and this method can still be used. As Linnaeus' works have few
or no illustrations and his diagnoses are elegantly brief, the Linnean
Society's collection is invaluable for determining the correct names of his
species.
 
Andrew K. Rindsberg
Geological Survey of Alabama