To properly fertilize and aerate your lawn in Parsippany, NJ, aerate in the fall (early October) and fertilize immediately after, ensuring the fertilizer penetrates the soil through the aeration holes. 

Here's a more detailed breakdown:

1. When to Aerate and Fertilize:

Timing:
Aerate your lawn in the fall (early October) for cool-season grasses like Kentucky bluegrass, fescue, and ryegrass, as this allows the roots to absorb nutrients before winter dormancy.

Why Fall?
Aeration in the fall helps loosen compacted soil, allowing air, water, and nutrients to reach the roots more effectively, which is crucial for a healthy lawn.

Avoid Spring Aeration:
Aerating in the spring can damage new grass shoots, so it's best to avoid it. 

2. How to Aerate:

Water the Lawn:
Water your lawn thoroughly the day before aerating to soften the soil and make it easier to penetrate. 

Choose an Aerator:
You can rent a core aerator (plug aerator) from a local rental center or hardware store. 

Aerate:
Go over the lawn in one direction, and then again in a perpendicular direction to ensure thorough aeration. 

Leave the Plugs:
The plugs of soil removed by the aerator can be left on the lawn, as they will decompose and return nutrients to the soil. 

3. How to Fertilize:

Apply Fertilizer:
Immediately after aerating, apply a fertilizer that's rich in nitrogen, phosphorus, and potassium (NPK).

Water After Fertilizing:
Water the lawn thoroughly after applying fertilizer to help it penetrate the soil and activate the nutrients.

Follow Package Instructions:
Always follow the instructions on the fertilizer package for proper application rates and timing. 

4. Additional Tips:

Overseeding:
If you have bare patches in your lawn, consider overseeding with grass seed after aerating and fertilizing. 

Topdressing:
Consider topdressing with a layer of compost or soil after aeration to further improve soil structure and fertility. 

Avoid Walking:
Avoid walking on the lawn for a few days after aerating and fertilizing to allow the seeds and fertilizer to settle and the soil to recover. 

Regular Mowing:
Continue to mow your lawn regularly, but avoid mowing too short, especially after fall aeration.