How Do I Mix Compost into Garden Soil?

My front yard was dug up to fix a sewer line. We mixed the soil before the winter with some peat moss and let the soil sink over the winter. There is clay in the soil for sure, but it's not that bad. Some tulips actually came up this spring.

I want to mix in compost and spread it back through some of the gardens bordering the house that have shrubs and small trees planted. Some gardens I won't mix in due to the better conditions of soil in those gardens. Has anyone ever dealt with this huge mound of dirt and how did you handle this large task?

Hardiness Zone: 6a

By krt4070 from Cleveland, OH