You can sift your compost through a very fine screen and simply sprinkle a layer on top. Applying compost in a wide ring directly below the dripline of a tree feeds the root system. When planting tree seedlings, blend some compost with existing soil as a soil enrichment. Compost helps to retain moisture. Compost builds sound root structure.
Compost makes clay soils porous so they drain.
Compost improves sandy soils moisture holding capacity. Compost attracts and feeds earthworms. Compost helps control soil erosion. Compost reduces plent stress from drought and freezing. Compost improves vitamin and mineral content in food.