Q:

According to J.R.R. Tolkien, who built the Hobbit structures?

I believe they are known for gardening, drinking ale, smoking leaf, and generally hanging about in their own neck of the woods, but I don't recall they are ever stated as being craftsmen. Is there a quote or a J.R.R.T. canon reference stating that the Hobbits built their own communities, or one that says they brought in outsiders to do the job? 

A:

The text of The Hobbit explicitly states that Bilbo's father built Bag End in the chapter "An Unexpected Party"

"The chance never arrived, until Bilbo Baggins was grown up, being about fifty years old or so, and living in the beautiful hobbit-hole built by his father, which I have just described for you, until he had in fact apparently settled down immovably."

The LOTR chapter "Concerning Hobbits" discusses the building habits of hobbits at great length, including a description of their building styles;

All Hobbits had originally lived in holes in the ground, or so they believed, and in such dwellings they still felt most at home; but in the course of time they had been obliged to adopt other forms of abode.
Actually in the Shire in Bilbo's days it was, as a rule, only the richest and the poorest Hobbits that maintained the old custom. The poorest went on living in burrows of the most primitive kind, mere holes indeed, with only one window or none; while the well-to-do still constructed more luxurious versions of the simple diggings of old. But suitable sites for these large and ramifying tunnels (or smials as they called them) were not everywhere to be found; and in the flats and the low-lying districts the Hobbits, as they multiplied, began to build above ground.
Indeed, even in the hilly regions and the older villages, such as Hobbiton or Tuckborough, or in the chief township of the Shire, Michel Delving on the White Downs, there were now many houses of wood, brick, or stone. These were specially favoured by millers, smiths, ropers, and cartwrights, and others of that sort; for even when they had holes to live in. Hobbits had long been accustomed to build sheds and workshops.

And

It is probable that the craft of building, as many other crafts beside, was derived from the Dúnedain. But the Hobbits may have learned it direct from the Elves, the teachers of Men in their youth. For the Elves of the High Kindred had not yet forsaken Middle-earth, and they dwelt still at that time at the Grey Havens away to the west, and in other places within reach of the Shire. Three Elf-towers of immemorial age were still to be seen on the Tower Hills beyond the western marches. They shone far off in the moonlight. The tallest was furthest away, standing alone upon a green mound. The Hobbits of the Westfarthing said that one could see the Sea from the lop of that tower; but no Hobbit had ever been known to climb it. Indeed, few Hobbits had ever seen or sailed upon the Sea, and fewer still had ever returned to report it. Most Hobbits regarded even rivers and small boats with deep misgivings, and not many of them could swim. And as the days of the Shire lengthened they spoke less and less with the Elves, and grew afraid of them, and distrustful of those that had dealings with them; and the Sea became a word of fear among them, and a token of death, and they turned their faces away from the hills in the west.
The craft of building may have come from Elves or Men, but the Hobbits used it in their own fashion. They did not go in for towers. Their houses were usually long, low, and comfortable. The oldest kind were, indeed, no more than built imitations of smials, thatched with dry grass or straw, or roofed with turves, and having walls somewhat bulged. That stage, however, belonged to the early days of the Shire, and hobbit-building had long since been altered, improved by devices, learned from Dwarves, or discovered by themselves. A preference for round windows, and even round doors, was the chief remaining peculiarity of hobbit-architecture.

