Genghis Khan left the cities to be ruled by their own people for the most part if they surrendered, which left them completely intact. The city would be required to pay a percentage of all goods to the Khan. In fact, this was substantially the Mongolian economy. For the most part, Mongols could not smelt, make pottery, craft with silk, mine, etc. Despite this, the entire Kingdom grew exponentially wealthy as peoples were conquered. It took a truly huge empire that spread across most of Asia, into the middle east, and into Europe. It would have encompassed more land if the heat didn't mess with their horses, men, and bows so badly. If the leaders did not surrender, or refused to pay tribute, there was no mercy. Cities could be razed. People were killed needlessly to instill fear. He could be brutal if it benefited him.

For the most part, conquered cities didn't need to produce military goods. They may have contributed arrows, but the Mongols mainly fought from horseback. They preferred to fight from distances as they believed getting blood on you would contaminate your soul. They conquered infantry and only used the troops they capture to lead a charge as a sacrifice to ease mongol losses. They had little need for heavy armor, swords, etc. In fact, their armor was very light and modtly covered their fronts to prevent retreat or to lighten the load. What they did enjoy were siege machines. The Mongols played a direct role in creating and furthering the catapult, flame thrower (gun powder with a slow burn), and cannons.

The Mongols also thoroughly pillaged towns. They would evacuate the town and systematically go building to building looking for anything valuable. Before Genghis Khan (pronounced jane-gis not gain-gis by the way), pillagers kept whatever they found. But under Genghis Khan, all of the booty was piled up and distributed by a shares allocation.

This is going beyond the question, but I thought I'd add how stable the land was that was conquered. Genghis Khan is largely shown as a barbarian in modern depictions. However, this is in a large part due to a play of Voltaire depicting him that way. He was using him as an allegory of the French king to avoid being prosecuted, but the image stuck to the great Khan. Genghis khan built and ensured safe roads, thousands of public schools, a writing system, freedom of religion, diplomatic immunity, paper money, and his influence is still reverberating through the modern world. They also assembled one of the largest sailing fleets in history, inspiring the British and Spanish armada. Edit: as I clarify later in this thread, he wasn't a nice guy. He was often brutal, but always cunning. He was constantly learning and was as elite a strategist as has lived.

Edit: to add another fascinating point related to your question, the armies of the Mongols spread out for miles. It could take days to ride from the left side to the right side, even in organized hunts as opposed to war. This was due to the horses needing to graze since everybody was mounted and each soldier had up to four or five horses. When they conquered an area, they often trampled crops so the land would return to grazing ground. They viewed the farmer peasants as little more than animals eating vegies and living in one area where their food was located. This was far different from the meat heavy diet of the Mongols.

All of this and more is available in the highly recommended and thoroughly captivating book "Genghis Khan and the making of the modern world." The audio book is equally captivating, and was recently on audible for $5. Currently $4 on Kindle http://www.amazon.com/Genghis-Khan-Making-Modern-World/dp/1491513705

My horde grows wealthy. Glad to see my vassals are showing their proper respect. I will not have to resort to violence for at least another month.

Wasn't it key that a city could surrender to the great Khan before hostilities broke out and pay tribute (tax)? Wouldn't this mean that with the conquests, there would be a steady string of income?

Edit: Thanks for the upvotes, but I'm as interested in sourced answers as the OP. There is good stuff here but sauce pleazze!!!

I can give light to part of this question.

With regards to supply lines, it really depends on what time period you're referring to, and which conquest/campaign, but there were some general trends.

One of the strengths of the Mongols was that they didn't have supply trains: because they were nomadic, their horses/ponies grazed. John Masson smith Jr. states that "the grazing made the horses independent of supply trains, and the horses in turn made the Mongols themselves independent... the army's horses provided both milk and blood for food." Though they could only get milk for part of the year, and blood was used as a last resort. They brought extra horses along that could be used as food as well.

They also sometimes brought along their other animals (goats and sheep mostly, though also cows and camels) that they milked and ate along the way.

Furthermore, they took supplies from the areas they invaded. As Desmond Martin explains, "After enemy country was reached it was expected that further provisions would be brought in by raiding parties. The Mongols looked to the territory before them rather to that behind to supply their wants."

Sources: Amitai-Preiss, Reuven and David O. Morgan, ed. The Mongol Empire and Its Legacy. Leiden: Brill, 1999. Martin, Desmond H. "The Mongol Army." The Journal of the Royal Asiatic Society of Great Britain and Ireland, no. 1 (April 1943):46-85. Smith, John Masson, Jr. "Ayn Jalut: Mamluk Success or Mongol Failure?" Harvard Journal of Asiatic Studies 44, no. 2 (December 1984): 307-345.

Follow up question, how was the economy in Mongol controlled cities? Could they be described as in a state of total war, feeding the Mongol Horde? I would imagine Genghis Khan would want to immediately allocate production for his military right after conquest.