Agricultural practices changed in part by necessity. I can only speak to my experiences growing up on a wheat farm in Kansas with the generation that survived still around to tell us about it.

The weather in the 1920's had some impact on what happened later in the 1930's. In the 1920s there was a good amount of rain and the farms were booming to the point that they were able to farm parcels of land that during normal cycles would be difficult at best. Often after harvest the preparation for next years crops involved plowing the stubble. This churning of the topsoil was seen as a need practice to help control weeds and to increase the speed of the breakdown of the organic material that would feed next years crops. The downside of this is the exposure/loss of the moisture trapped in the soil. Additionally there was a heavy push for growing cash crops (wheat primarily in the area I grew up in) and the incentive to rotate crops or fallow (a season without crops) fields was a good deal lower. So the topsoil started to lose it's reserve of moisture (and often it's cultures of beneficial microbes) while calamitously being stressed by growing more crops than before.

One of the first lessons learned while the dust was still flying was that rows of drought resistant trees could help protect fields from the harsh winds and even help hold some moisture by collecting snow drifts. The next lesson learned was the idea of leaving stubble for cover during fallow years. Crop rotation now included a different variety of plants that grew at different cycles meaning that often you could still get 3 crops every 4 years. Marginal ground were more selectively cultivated. The concept of planting to prevent erosion along with other soil conservation techniques began to come into play.

There were massive soil conservation educational campaigns that persisted for over 50 years (as I remember them as a kid in the 1980s). Many of the farm ponds were dug well before the 1930s as I remember hearing about what years ponds dried up after the "dirty 30's". Yes many lakes were added but many of those were not put in directly after the 30's, one close to my family farm wasn't put in until the late 70's. Often these were put in with some flood control in mind which seems opposite of what you would think. Indeed most of the bigger man made lakes in my area of Kansas really aren't used for agriculture at all.

Now often you will hear of zero-till or no-till crops where the soil is not disturbed at all between plantings and weed control comes in the form of the stubble/straw covering the soil during the fallow times and herbicide. The equipment can now plant in the somewhat harder solid without the need for a series of implements to be drug over them to prep the field for planting. Additionally the varieties of crops have evolved greatly via selective breeding and now with some very targeted genetic engineering (not necessarily modifications, but targeted breeding to get the right gene expressions desired) that have resulted in plants that can yield more grain with less waste and better tolerances for drought and disease.

There have been some similar droughts and dry times in the area since the 1930's. In 1988 some areas saw a return of the dust storms. I asked survivors of the Dust Bowl how the storms of 88 compared because to me as a child they seemed very bad to me. All of them said that the 88 storms were mild in comparison. Since then there was a stretch where many of the Dust Bowl records were broken, but the improvements to how the land is/was farmed prevented the disasters of the Dust Bowl from returning.