Incorporating compost-amended topsoil, well-aged compost, calcined clay and/or expanded shale, are recommended strategies for improving soil infiltration rates. In addition, topping the garden with annual application of organic mulch is a key ingredient for reducing compaction and improving soil quality and infiltration capacity. This will, in turn, improve plant growth and root systems which increase the ability of the soil to absorb water over time.
Adding sand in insufficient quantities can result in a concrete-like soil texture that does not drain; therefore adding sand is NOT recommended.
For more detailed soil amendment and mulching recommendations see Conquer Compacted Soils.
For guidance on fertilizing your yard see Fertilizer Management.