Use the level to determine which areas of your lawn are lower than the rest.
Pour several inches of lawn sand in the lower areas.
Compact the sand with the hand tamper. Position the tamper over the sand and pound on top of it to compact and flatten the area.
Add a few more inches of sand and flatten again with the hand tamper until the ground appears to be level.
Check the evenness of the ground with your level. Add more sand and flatten with the hand tamper until you achieve even ground.