For literally hundreds of thousands of years, humans existed as nomadic bands of hunter-gatherers, living off what plant and animal sources that they could find as they wandered from place to place.  The amount of time that a wandering group settled in a particular place was certainly connected to how long the local resources lasted;  some places were more bountiful than others.  More work could be put into shelter.

Who knows how the first "farmers" figured out that some of a plant could be persuaded to grow into an entire new plant?  It seems likely that this started with the understanding that nuts were the source of new trees.  It seems like long before the seed-planting of crop plants, humans were expanding the numbers of useful trees in forests of Europe and the Americas, often burning off trees that were not useful to them and "encouraging" the growth of others.  The idea that plants grew from small bits of a bigger plant was out there, but forest management was a longterm affair for groups that would wander through a large forested territory.  The growth of other crop plants that could be done season-to-season was potentially something to be done in more wide-open areas with rich soil was probably not so easy to work out.  Maybe a curious ancestor noticed sprouts in the village's trash pile and worked out what discards were growing into new edible plants, and gradually worked out how to get that to happen on a scale that could actually feed a village.

It appears that these first steps happened in those particular areas with the right conditions for cultivation of local wild plants and raising some local animals.  Areas that flooded regularly, bringing in new nutrients to the fields, or areas where fertile lands were always closel by as current fields got depleted, were ideal for the development of early agriculture.  These sorts of places are spread around the world.

Comparisons of hunter-gatherer societies that still exist with basic farming communities suggests that agriculture does, on average, involve a lot more individual work than the more ancient approach, but the potential of agriculture - it is more reliable and can supply much more nutrition to a concentrated group of consumers - looks like it outweighed that disadvantage where it was feasible to do it.  Surviving hunter-gatherer groups live in places where agriculture would have had a hard time developing, even though modern mechanized techniques can sometimes make the land usable (briefly).
 

 There are constraints on the sizes of hunter-gatherer groups, associated with the amount of food that can be gathered and the general richness of the environment that the groups wander through.  In soil-rich areas with a lot of seasonal plant foods, larger groups could be supported, settled for decent amounts of time before needing to move on.

Being able to produce food from captive animals and cultivated plants reduced the need to wander, producing the potential for settled villages, towns, eventually cities.  Trading, probably already important for nomadic groups, became even more important, as materials for implements and different foods could be shared to improve settlements' prospects even more.  Archeological evidence from many sources indicates widespread movement of goods around the ancient world. 

Agriculture is of course a type of technology, and technology advances as people experiment and see what works and what doesn't.  Tilling, the preparation of soil for planting, is not just using plows to turn over the surface - any adjustment to the surface can be important.  Sharp wooden implements eventually gave way to various metals, and manpower was eventually replaced by draught animals (where they were available), the machines.  In recent years, attention has been drawn to the negative effects of tilling:  increased erosion and release of the greenhouse gas carbon dioxide.  No-till farming is a possible alternative, but requires even more sophisticated technology.

Many of the origination sites for agriculture have had features that easily supported planting and harvesting:  warmth, regular rainfall, rich soil that could be tilled regularly (and often seasonal flooding to recharge the nutrient levels).  All of these aspects were less reliable is areas that agriculture spread to. 

Irrigation techniques developed to deliver water in areas where rainfall could not be depended upon, usually by diverting some water from a flowing system nearby, or by drawing it up from an aquifer.  Drip irrigation uses a slow-release mechanism - originally water in containers of unglazed pottery that would leach water into the surrounding soil, now usually a network of pipes with small holes in them.

Continuous use of an area year after year can deplete the soil of the nutrients plants need.  Fertilizers have been in use since ancient times, usually accessible human and/or animal wastes or processing leftovers.  Slash-and-burn techniques are an ancient response - cut down a forested area, burn the remnants, plant the cleared land until it's depleted, and move on.  In places with lots of land and very few people, this works reasonably well.  For modern farming, too much land with not enough recovery time (it can take 10 to 20 years for a plot to regenerate) makes it an unsustainable approach.

Back in the chapter about evolution, it was mentioned that Darwin had experience with selective breeding of pigeons - by picking the individuals with the features you were trying to accentuate and breeding just those individuals, generation by generation you can change the basic nature of the whole group.  Once natural selection became part of the basic language of biology, the term for selective breeding became artificial selection.  In domesticated species, it means breeding individuals with the best of preferred features.  In plants, it involves just planting seeds from the plants that are showing the best of whatever feature you want more of - faster growth, bigger yield, better growth with limited water, whatever trait the breeder decides to shift.  In animals, it involved not just food-related features but characteristics that make animals easy to get along with.  What is happening, just as in "regular" evolution, is a change over time in the gene pool, making useful alleles much more common.  Over time, the same sort of shifts that we see in nature separate crop plants from their ancestral species:  modern cows, corn, rice, etc., are considered different species from the wild varieties they originated from. 
 

Many modern agricultural techniques are said to have originated in Europe of the Middle Ages, although variations can be found throughout the world - where certain technologies "started" is often debatable.  It's not often known if certain approaches arose independently in different places, or the ideas were widely shared.  Technology can spread that way - just hearing someone describe a technology that they have seen somewhere else can provide the inspiration to "reinvent" it locally.  The innovations commonly associated with Medieval Europe are the modern harness for draught animals, the wheeled plow, the flail, the water wheel for irrigation feeds and driving processing machninery, and shifting crops in multi-year rotations to regenerate the soil.

More modern development can be tied to sophisticated distribution systems - the seasonal limitations that used to be just part of reality don't exist for many products.  Food preservation has progressed well beyond salting and below-ground storage.  Canning allowed longterm preservation that could be transported. Refrigeration, especially refrigeration in transit, was a huge innovation and frozen foods have largely replaced canned foods.  Products can be moved easily around the globe with minimal spoilage loss. 

Mechanization drives a lot of modern farming, replacing human workers with high-efficiency machines.  In the United States, farm workers were 41% of the population at the beginning of the 20th Century;  by the end, that number had dropped to 2%. 

Some of the modern answers to basic questions have led to the question of how much usage of resources is too much usage, such as large-scale water diversions, aquifers drained faster than they can refill, soil erosion on a massive scale, etc.

Another innovation is artificial fertilizers produced on a commercial scale, profiding the phosphates and nitrates that crops require.  The downside to these is runoff, carrying plant-boosting chemicals into water systems that increase algae loads and disrupt both freshwater and nearshore ocean ecosystems.

A host of pesticides have been developed to deal with living things that interfere with the growth and health of crop plants and animals.  Since the target is alive, evolution commonly produces resistant varieties of pests, and the arms race continues.  Antibiotics are administered to combat bacterial disease, but it has been found in many types of livestock to boost growth;  in either case, antibiotic resistance in the bacteria is fostered.

All of these innovations have driven a shift toward what is sometimes called factory farming, agriculture on huge scales by corporate entities.  Crop farming has moved toward monocultures, not just the same crops but the same genetic version of a crop.  Livestock are concentrated in large facilities that often pen animals in very limited space where they can barely move.  Markets for some commodities get narrowed to just a few sources, raising food prices in the face of no competition.  A movement for small-scale, sustainable agriculture or organic farming that tries to use no artificial chemical aids cannot really meet the demands of the human populations.

Genetic modification is no longer a byproduct of selective breeding, but something that can be done on a gene-by-gene basis, introducing specific alleles for specific abilities into crop strains.  The alleles often originate in plants or animals that are not used for food but have a feature useful in agriculture, such as resistance to frost or drought, but moving an allele means introducing the protein product of that code.  Testing is usually rigorous, but consumption is a longscale thing, and testing can only practically look for shortscale effects.

One type of food that stayed the in hunter-gatherer realm long after the others became agriculture is fish and seafood, but the demands of modern human populations have depleted most of those sources (although fish depletions have led to larger populations of things like lobsters).  Today, about half of such foods are produced through aquaculture, largely with various approaches for penning and raising aquatic stocks.  This also comes with a variety of ecological impacts.  Hydroponics is a an approach to growing terrestrial crops in nutrient broths - aquaponics uses aquaculture products to supply that broth.