Hay is one of the resources you will need for certain things like beds in Going Medieval. So to get hay, you will first need to find grass, as shown below.
You can find grass growing in Going Medieval in various places on the map, just have a look around, and you are sure to find it. When you find the grass, you can have it harvested by your settlers by marking it with the cut plants key.
To do this, hit the j key and then mark the tall grass by highlighting it. After this, your villagers will soon run over and cut the plants down and bring them back to your stockpile as hay.
Related: How to bury the dead in Going Medieval
If you want to speed this process up, you will need to go into your job tab at the top left of your screen and locate the cut plants key and increase the number under it to one.
Doing so will set the job of cutting plants to be the highest priority for that settler. You should also make sure to send only the best to do this job, and you can find this out by hovering the cursor over the job.
In short, settlers with a high-level botany skill will be the best to cut plants, otherwise they might fail and destroy the plant.
For more on Going Medieval, check out How to make smoked meat in Going Medieval and How to cook food in Going Medieval