help - turn straw bedding/hay from the barn into compost

hey permies
i am confused bout how to turn straw bedding/hay from the barn into compost.  For instance, if i use the deep litter method for goats all winter and muck out the barn in the spring i know in theory that soiled straw has a lot of potential for the garden but... now what?  put it in a pile and flip it with a pitch fork every so often? or put it directly in the garden in the spring?  or put it on the garden in fall?
forgive me if this is a dumb question.
thank you

I put the bedding in a big pile somewhere I want to improve the soil.  I plant squash seeds in it.  After the squash are harvested, I move the pile to where it's going to become soil.  It's usually soil by now, but if it needs more work, I put it back in a pile and then distribute the new soil in spring.