It's a good question, but as stated in this answer, there is no canon information on this issue. The Hobbit doesn't go into how Smaug gathered all his treasure into one place, and The Lord of the Rings hardly mentions Smaug's hoard at all.
Maybe he picked up the gold with his feet and carried it laboriously - possibly piece by piece - into the Mountain. As we can see in this picture from Tolkien, Smaug had four legs with well-defined claws:
The fact that he immediately missed the cup Bilbo stole suggests that he keeps careful account of his treasure, probably by handling it regularly (I think there was a quote to confirm this, but I can't find it now) - so he may well be able to pick up gold ingots etc. with those feet. And he had a lot of years in which to transport the treasure of Dale into the Mountain!
Maybe he had slaves to do the carrying for him. He might have terrorised some passing mortals - perhaps even some of the Dwarves from Dale - into carrying 'his' gold into the Mountain for him. Under the threat of death, they'd be too terrified not to oblige; and then he could always eat them afterwards anyway.