How is the Cost of Land determined when you purchased an existing home?

Generally the county assessor where your property is located designates between land and building.  See if you can search for your county's assessors office and see how they have it split up.  

the proper way is to allocate the purchase costs including closing costs based on the ratio of the FMV of the land to the FMV of the entire property.   how do you determine FMV of land?  there are no official ways.  if you are assessed taxes based on the FMV of each perhaps the last tax bill which should be a public record will have the relative values. but you need to check. where I live land is valued at a lower % of FMV than the building but the bill only reports the total assesses value. another source is a realtor in your area.  finally, I would guess that many just pull a number out of the air. 

Thanks I found that the cost of the land is generally a 20/80 ratio to the cost of the home or building.  More than 20 if in a high valued region i.e. costal CA versus a midwestern city or vice versa.