How can agriculture spread?
See explanation below.
There are several ways this question could be answered depending on what is meany by spread.
Agricultural ideas and practices are spread when people move to new areas, when one group trades with another group, and generally speaking when groups come into contact with one another. Purposefully or not, ideas are shared and technologies and new species may accidentally be introduced.
Origin and spread of different crops:
For example, the Pilgrims in the United States learned to plant corn, squash, and beans together to maintain soil fertility from the Wampanoag. The use of animal drawn plows spread from Egypt south to Sudan.
The image below shows the spread of potato cultivation across the globe:
Ancient forms of drip irrigation have been found in Egypt and Afghanistan. In the 1920s Germans were using perforated pipes for irrigation, the first efficient drip irrigation system was developed in Israel and spread to the US and Australia in the 1960s. You can read more about how drip irrigation has spread here.
Today, agricultural ideas spread through the internet, TV, travel and tourism, international conferences on agriculture that are held to attract people from all over the world, and when companies purposefully travel to sell their products and technologies to new areas.