What were the new farming methods and technology introduced during the agricultural revolution in the middle ages and what was its effect then?
The explanation should be based upon how it affected Population and also explain how trade revived.
The primary innovations during the Agricultural revolution of the High Middle Ages were the three field system, the development of a harness that allowed the use of horses rather than oxen to pull plows, and the heavy wheeled plow.
The three field system allowed for the production of more crops and postponed (but did not prevent) soil depletion. The system consisted of planting wheat in one field, barley or oats in a second field, and allowing the third field to lie fallow--unplanted. During the next planting season, the fields were rotated, so that each field was allowed to remain fallow once every three seasons.
For many years, oxen were used to pull plows to till fields. Horses could work twice as fast as oxen and therefore plow twice as much land; however the harness used for horses was the same used for oxen, which tended to strangle the horse at the jugular vein, and caused the horse to rear back violently. A new harness was developed which fit across the horse's shoulders rather than its neck. This allowed the use of horses to till soil and thus led to increased production.
The heavy wheeled plow allowed for deeper tilling down into the rich sub-soil. This also led to increased production. Because the plow was so cumbersome, it could not easily be turned around, and led to the development of elongated fields, often farmed in common with other families.
The production of more food allowed people to be healthier and as a result, more people survived opportunistic diseases which otherwise might kill them. Earlier, production averaged three seeds for each seed planted. With new techniques, the amount produced doubled.
The relationship to revived trade is indirect at best. Increased production meant a decrease in the price of food, as a result of which people had more money to spend on other items. With more money to spend, specialization and trade developed and towns, which had disappeared from the landscape, reappeared.