How did the Gold Plates Get from Mesoamerica to the State of New York?
Evidence indicates that originality the Book of Mormon plates were in Mesoamerica.
Moroni was obliviously in charge of the Book of Mormon plates thus he would have been the one instructed to deposit the plates in the New York hill now called Cumorah.
We have not as of 2010 A.D. been given any revelation or information on exactly how or where Moroni traveled to in order to be able to get the plates from Mesoamerica to the Hill Cumorah in the State of New York.
The last of the Nephite people were wiped out about A.D. 385 (Mormon 6:5).
Moroni wandered "whithersoever I can for the safety of min own life" to avoid being captured and killed by the Lamanites. (Moroni 1:3)
At the end of his record Moroni tells us that "more than four hundred and twenty years have passed away since the sign was given of the coming of Christ". (Moroni 10:1)
Moroni was still alive for another 36 years after the destruction of his people (421 – 385 = 36).
If Moroni traveled this distance on foot, Moroni would have had more than enough time for him to travel by foot from Mesoamerica to the state of New York.
Also for example, a mid-sixteenth century, David Ingram, a shipwrecked English sailor. Walked in 11 months through completely strange Indian Territory from Tampico, Mexico, to the St. John River, at the present border between Maine and Canada. His remarkable journey in 1568 A.D., would have been about the same distance as Moroni's if he took the approximatiey same route.
So Moroni's getting the plates to New York even under his own power [in 36 years] would be completely possible.
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Did Moroni have help moving the record?
A Pre-Columbus Iron Wagon Found in New York.
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Additional Information
FairMormon Answers - How did the gold plates get from Mesoamerica to New York?)