random_man
Throughout it's history, the US government has attempted to support farmers and agriculture, to ensure a stable and affordable food supply and support the rural economy. This support has taken various forms throughout the years, and stepped up a lot during and after the Great Depression.
I'm not sure about precise dates and all that, so I'll speak in general terms.
On of the first things the US government did for farmers was to establish the department of agriculture, and later, in 1916, the Farm Credit system. At the time, banks were largely in urban areas, and the farm credit system provided credit to farmers and rural citizens to improve and expand their farms.
Another thing that the US government has done is the establishment of a series of subsidies and incentives. I'm not real clear on the early forms of these, you'll have to look it up, but basically, the US Government has at times given farmers money directly, and also purchased agricultural products in an effort to support farm income. More recently, farm subsidies have mainly taken 2 forms: cost-sharing for crop insurance, and directed grants. Cost sharing for crop insurance, means that the feds pay a portion of the premiums for crop insurance that the farmer buys. Then, if the farmer incurs a loss, the crop insurance policy will reimburse the farmer for a portion of that loss. Here's an example. An apple grower buys crop insurance against hail damage to his crop. He splits the premium cost with the fed govt. A hailstorm damages his crop by 75%. The insurance company reimburses him for half of the value of what he lost. The farmer doesn't make much money that year, but at least he now has some money to help pay his expenses. He is able to continue farming and grow apples.
Another type of subsidy are directed grants. Here's an example: A new regulation passes that requires dairy farms to have better manure storage in order to protect water resources. This enhanced manure storage might cost a farmer $100,000 - more than he can afford. So the USDA offers a 50% cost-share to help defray some of the cost of this new regulation. The farmer builds the manure storage, the fed govt pays part of the cost, and the water resource is better protected.
Other things that the government has done to support farmers include: funding agricultural research; and supporting development of export markets.
Contrary to popular belief, there are no US federal programs that pay farmers not to grow food. (I can't speak to what may have happened in the past, but there are no such programs today). The one program that does pay farmers not to cultivate certain land, is called the Conservation Reserve Program, which pays farmers to not cultivate environmentally sensitive areas, such as near streams or land that is highly erodible, but the purpose is protecting the environment, not reducing production. (And it's been cut back in recent farm bills).