Hay, like other farm and garden plant waste, is an ideal component of compost. It is in its natural state, which all or at least most compost material should be, and it does not contain any animal products. But hay by itself should not be the only or even primary addition to your compost pile. For a compost pile to break down material effectively, it needs a roughly equal mixture of dry material like plant waste and moist material like kitchen food scraps. A compost pile with the right combination of wet and dry material has the moisture level of a wrung-out sponge.
Examine the hay for seed and remove as much as you can. The seed will not break down in the compost pile, and it will germinate once the humus is spread over your garden.
Cut the hay into small pieces. The smaller the pieces, the more quickly they will break down into humus.
Spray the cut hay pieces with water from your hose to moisten them.
Spread the cut hay pieces over the top of the compost pile.
Use a shovel or stick to turn the compost pile and mix its ingredients thoroughly so that the hay is evenly distributed throughout the pile. Continue to turn the pile whenever you add more material or at least once weekly--the more often you turn the pile, the more quickly the contents will decompose.
Check the pile's moisture level the next day. If it is too dry (drier than a wrung-out sponge), add wet material such as vegetable or fruit kitchen waste. If you have none on hand, add a cup of water daily (turn the pile each time you add water) until the moisture level is appropriate or you have more kitchen waste to add.