Low spots and dips in you lawn can be just slight visual imperfections or they can be hazards depending on the severity. Soil settles at different rates and for a variety of reasons over time. Correcting a a depression in a lawn is a relatively simple task and can be treated much like reseeding a patch of lawn but with a little extra soil or compost needed to fill the void.
Rake up much of the grass and thatch that cover the depression in the soil and discard. Pull up the large stolons and runners by hand and discard those as well. Some root and grass material will not be a problem. Just pull up the bulk of the thick material so that the soil is partially visible.
Fill in the depression with compost and tamp down with the back of a shovel or your feet. Fill in more compost to create an area level with or just slightly proud of the surrounding soil. If the depression is deep or covers a large area, use regular garden soil to fill in the bulk of the low spot and cover that with an inch or more of the quality compost to be the seed bed.
Water the area well and allow the water to percolate down into the soil for at least 10 minutes or so. The soil will compress slightly, so add more compost to bring the area level again with the surrounding soil.
Sprinkle some lawn-starter fertilizer over the compost and use a rake to work that into the top half-inch of soil and spread it evenly. Sow the grass seed over the fertilizer to cover the compost evenly with a single layer of grass seed. Sprinkle a few handfuls of compost over that to partially cover the grass seed.
Water the area slowly and deeply with the hose nozzle set to a light mist or gentle rain so as not to displace the compost, seed and fertilizer. Keep the area moist at all times with daily or twice daily watering for roughly two weeks until the grass has germinated and established roots.
Keep all foot and paw traffic off the seeded area by staking and roping it off. Wait three weeks before using a lawn mower on the area to prevent the tender roots from being disturbed.