There has definitely been a lot of discussion around this. The "classic model" for the development of agriculture in the Near East is sort of depersonalized. This derives largely from the excavations at the site of Abu Hureyra (under Lake Assad now), which was a pioneer in a lot of archaeobotany. Basically what was found was that wild grown wheat made up an important part of the diet in the region well before the transition to agriculture, and the transition from wild wheat to domesticated wheat was not instantaneous but also fairly quick. The difference, by the way, is the strength of the rachis, or little stem that holds the seed to the stalk. In wild wheat the rachis naturally weakens and drops the seed when it ripens, but in domesticated it stays strong, which in practical terms allows someone to collect the entire stalk and harvest the seeds in a controlled situation, while with wild wheat more of the seeds would fall to the ground before harvesting.

I think it is easiest to think of the transition in mathematics terms: imagine you have a little stand of wheat you use as part of your subsistence strategy, and every year after harvesting you throw some of the seeds back in the ground (that seeds become plants is understood by hunter gatherers the world over). Of these plants, one in a thousand have the mutation that makes them domesticated, but that one plant will yield five times more seeds than a wild one because of how much easier it is to harvest. Thus in the first year one of a thousand plants are domesticated, but five of a thousand seeds you harvest are domesticated, meaning that the next year five of a thousand plants are domesticated, and then twenty five, etc. While this is happening, the plants are yielding higher and higher harvest due to the advantages of domesticated wheat, more and more of the food is coming from it, and thus the community orients more and more of its subsistence activity towards cultivating wheat. Soon enough, with nobody intending it, your hunter gatherer community has transformed into a farming one.

Of course around this process there is a whole host of questions that develop. For one, it assumes a sort of homo economicus approach to human behavior that doesn't actually match existing hunter gatherer communities--the classic example are the !Kung of the Kalahari, who can expend enormous amounts of energy on hunting animals even though mongongo nuts are nutritious, plentiful and easy to gather. And so an argument goes that other subsistence strategies had hit a bump--a finger has often been pointed at the Younger Dryas, a climate change event of round about 10,000 BCE that caused an intense period of cooling and drying. Others point towards cultural factors, which is the key to Klaus Schmidt's theories around Gobekli Tepe, a large standing site in southern Turkey that preceded agriculture. Perhaps, in this theory, growing social complexity had led to agriculture, rather than the other way around. It is no exaggerating to say that literally every archaeological theory to gain popularity has been applied to explaining this.

But of course everything I said applies only to a smallish are in the Fertile Crescent, and doesn't really explain how people in Germany started planting. This question is in no way less fraught than that of the initial development of agriculture. One theory is a migration model: the yield of agriculture tends to be patterned around period of booms and busts. A year of plenty and a year of dearth. This makes the sort of natural population planning that foragers employ difficult, leading to a tendency to rapidly outstrip a given area's carrying capacity (note, this point is contentious and over simplified). And so what is there t do but to found another farming village a few miles away. Rinse, lather and repeat over the generations. One might also add cultural factors to this, in which the idea of setting out on one's own is valued: this works very well for the expansion of the Lapita into the south Pacific, as the settlement patterns tended towards the founding of communities on new islands rather than more intensely settling already settled islands. But one way or another, so the theory goes, farmers were largely pushing into new lands rather than hunter gatherers becoming farmers.

But don't worry, there is disagreement on this! Another camp will point towards continuity in patterns of place value (eg foragers depositing stuff in a particular site are followed by agriculturalists depositing the same things at the same sites) and patterns of exchange (ie, inter community connections are undisturbed). The point following this is that local cultures are not destroyed, but rather picked up agriculture as another aspect of its culture, thus the Neolithic should be seen as a transformation of the Paleolithic rather than a replacement.

A third camp sees value to both sides and argues that the truth is somewhere in between which, frankly, is not very helpful.

One reason this becomes such a contentious topic is that the arguments can be rather easily turned around. Early agricultural settlement in Greece, for example, seems to be an importation of the entire "Neolithic package" of domesticated crops, animals and tools wholesale rather than a piecemeal and gradual adoption of different aspects at different times. A clear argument in favor of the migration camp! But wait, comes the counter does this mean that where the entire package is not imported (as, say, in the upper Balkans and Carpathian Basin) then there was no migration? Arguments go either way.

Added to this whole confusion is that the focus is overwhelmingly on the development of agriculture in the Fertile Crescent and spread into Europe. But agriculture developed and spread several times in different places: off the top of my head, in the Andes, in the Mexican Highlands, in the New Guinea Highlands, and China. Until this imbalance is corrected we won't get a very good image of agriculture's rise and spread in general rather than specific. And of course this all becomes even more confusing when you start to add more critical frameworks than simple developmental culture history. It is a real nesting doll of issues, which one of which opens up to reveal another, equally complex issue.

So, for sources, I would recommend Peter Bellwoood's First Farmers as probably the best introduction, as I don't know of any other single volume work that that synthesizes so much data and many perspectives. But know that Bellwood, perhaps because he mainly studies Southeast Asia, is very much in the migration camp, and so you should also read the critical reviews, which are numerous and often lengthy.

One hypothesis is that people developed agriculture to have a steady supply of alcoholic beverages. Is this idea very popular among mainstream historians/archaeologists these days?