How do I get rid of hay weeds in my garden?

if This is in your flower beds, I cut the weeds as close to ground as possible, cover with newspaper and mulch over the top.

In my experience, hay has weed and grass seeds in it that sprout in the garden. Fallen leaves or pine needles make great natural mulches! Or you can always purchase wood mulch!

Actually you should use straw (oats), not hay (grass) for mulching. But you can make the best of things by raking back the hay and laying several layers of newspaper on the ground, then put the hay back and add a few more inches of straw. The newspaper will prevent the grass from growing by eliminating light, and new seeds won't germinate. You should keep at least 4 inches of mulch on your garden to help keep weeds and grass from growing. Add more as it decomposes. I like to use my grass clippings instead of straw; you can use less because it compacts and keeps weeds from germinating and helps keep the soil moist. You also have a steady supply during the growing season. After several years your soil will be beautiful black topsoil from adding all that grass that decomposes.

I've used hay as mulch and liked it quite a bit but the thing to remember is to use hay that hasn't gone to seed.

Getting rid of them will involve lots of pulling by hand unless you want to use harsh chemicals which is something I DO NOT recommend.