Stardew Valley is all about managing your farm and if you have animals, you will need to feed them hay. Hay is incredibly easy to come across, but if you don't have a building set up to store it, you can't actually acquire it outside of buying it. Here's how you can collect hay and what you need to do beforehand.
How to get Hay
Hay can be acquired by cutting grass with a scythe, but only if you have a silo with space to store it. Silos can be built by the Carpenter, for the low cost of 100 stone, 10 clay, 5 Copper Bars, and 100G. A single Silo can hold up to 240 pieces of Hay. Cutting grass has a 50% chance to give hay with the normal scythe and 75% chance with the Golden Scythe. Any hay obtained from cutting grass on your farm with the scythe is automatically sent to the silo, as long as there is space. If the silo is full, you won't obtain hay from cutting grass.
Grass will occasionally start growing on your farm randomly during most seasons, although it is significantly less likely during winter. You can start a grass patch yourself by using a grass starter, which can be purchased for 100G from Pierre's or crafted using 10 fiber after purchasing the recipe from Pierre's for 1,000G.