You just throw whatever you have on the garden and turn it in. I have done this many times with manure mixed with sawdust, shavings or straw and sometimes straight manure. I spread it in the spring and turned it into the soil. Certified organic growers have to compost manure, by the way, or spread it 120 days before harvest. Sheet composting is fine as long as there is a good supply of nitrogen.
Manure is the usual supplier of nitrogen.
If you spread just sawdust which is a material high in carbon, The soil microorganisms will be overworked for a while breaking down the material and crops may suffer from a lack of fertility. Some say the organic material has robed the soil nitrogen. It is more accurate to say borrowed as once the soil is back in balance it will benefit from the additional organic material that, for a time, caused an imbalance. N ratio of sawdust is 400 to 1 while for rotted manure it is 20 to 1 and young sweet clover is 12 to 1. All of these materials once composted are pretty close to 50 to 1.