It looks like you have some crab grass. It will die after a frost or two. It produces millions of seeds, so it will be back next year. The only way to prevent it is to have a thick turf as the seeds needs to be on sunny dirt to germinate.

The only thing you can do now is to have your lawn core aerated, overseeded with a tall fescue and fertilized. What happens is many of the seeds fall in the holes and will germinate by the spring. They form little fescue plugs which will spread out and fill in your lawn over time. At least ideally that's what will happen.

You can take a few plug samples and send them to your county cooperative extension (Or whatever you have in your county/state) in for analysis. They'll recommend a treatment plan to make your soil good for growing grass.

It will take years for you to get where your neighbors yard is, but this is the best start.

You'll need to get a local landscaper to do this and for half an acre, it will probably cost between 3 and 5 hundred or so.

Aside from what work you do on your present lawn, unless a nursery has suggested a winter-type of fertilizer it is best to put off feeding the lawn until the spring when it will generate growth and spreading of the lawn.

You have given your lawn no water....no food...from spring through summer, now into fall.
And you ask what is wrong with your lawn.

Without being rude....I suggest the answer lies in the mirror.
Grass is no different than other plants...there's just lots of them. Like yourself, grass needs food to grow and look good. It needs water ---the proper amount, at the proper time to foster good growth.
Too little water, the roots grow short.....too much water, the roots grow short
The sun then has a field day ruining what is left and the weeds, which don't need as much water....but enjoy lots of sun, will love it. Hence the reason to give weeds as much shade as you can. Their seeds wont germinate as readily.
Do not water according to any schedule....water only as the lawn needs it. Rain notwithstanding.

Let your lawn grow higher..3" - 3 1/2" high....this height will shade out weed seeds---including crabgrass, and over time....two --three....+ years, the lawn will prove to be a good one.

Generally, we decide when we wish our plants to go into natural dormancy.....and grass is no different.
It is commonly accepted in northern zones to not apply fertilizer to lawns after 6 weeks before a hard frost is expected. Usually, mid August to mid September.
The reason being we don't want the grass to grow soft when a hard frost arrives to kill it.

Soil temperatures are fast losing the ability to germinate new grsss. A winter type fertilizer is being pushed by the people who sell it.....and even they cant agree on just how much nitrogen should the food contain.

You will get advice from many here from all over the country. Much of this advice is generic or not for your area.

My thoughts are you should ask your neighbor for advice.

Generally I hate the idea of core aerating for any reason...but kidhorn has a point. Seed does seem to come up in the core holes better than outside. I suspect a couple reasons, but I'd rather wait to discuss those.

What he goes on to say isn't quite right. Fescue plants will not spread to fill in. Fescue plants grow independently and only spread with the speed of glacial retreat. In fact today the glaciers are retreating much faster than fescue grass spreads. If you want a grass that will fill in, then what you want is Kentucky bluegrass.

I also disagree that it will take years to have a lawn like your neighbors. If your weather holds, you can get an excellent start on it now.

Here are some basics everyone should have handy. You will tailor these to your own specifications, but the general ideas are all here.

Basics of Lawn Care

After reading numerous books and magazines on lawn care, caring for lawns at seven houses in my life, and reading numerous forums where real people write in to discuss their successes and failures, I have decided to side with the real people and dispense with the book and magazine authors. I don't know what star their planet rotates around but it's not mine. With that in mind, here is the collected wisdom of the Internet savvy homeowners and lawn care professionals summarized in a few words. If you follow the advice here you will have conquered at least 50% of all lawn problems. Once you have these three elements mastered, then you can worry about weeds (if you have any), dog spots, and striping your lawn. But if you are not doing these three things, they will be the first three things suggested for you to correct.

Watering
Water deeply and infrequently. Deeply means at least an hour in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. Do not spread this out and water for 10 minutes every day. If your grass looks dry before the month/week is up, water longer next time. If that does not work, then you might have to water more than once per week during the summer's hottest period. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.

You will have to learn to judge when to water your own lawn. If you live in Las Vegas your watering will be different than if you live in Vermont. Adjust your watering to your type of grass, humidity, wind, and soil type. It is worth noting that this technique is used successfully by professionals in Phoenix, so...just sayin.' The other factors make a difference. If you normally water 1 inch per week and you get 1/2 inch of rain, then adjust and water only 1/2 inch that week.

Mowing
Every week mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. However, bermuda, centipede, and bent grasses will become the most dense when they are mowed at the lowest setting on your mower. In fact there are special mowers that can mow these grasses down to 1/16 inch. Dense grass shades out weeds, keeps the soil cooler, and uses less water than thin grass. Tall grass can feed the deep roots you developed in #1 above. Tall grass does not grow faster than short grass nor does it look shaggy sooner. Once all your grass is at the same height, tall grass just looks plush. One last exception is Kentucky bluegrass. The experts mow it at 3.5 inches (one notch below the highest setting).

Fertilizing
Fertilize regularly. I fertilize 5 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above. Follow the directions on the bag and do not overdo it. If you are using chemical fertilizers, too little is better than too much. If you are using organic fertilizers, it is the other way around. At this point you do not have to worry about weed and feed products - remember at this point you are just trying to grow grass, not perfect it. Besides once you are doing these three things correctly, your weed problems should go away without herbicide.

Now that you're an expert on lawn care, here is my advice. You have really done a number on your soil by not watering. Healthy soil depends on having a huge population of beneficial microbes. Then need food but mostly water to survive. By allowing the soil to dry out extensively, those populations have dwindled. So how to recover? This will sound crazy but it works. Spray any clear shampoo at a rate of at least 3 ounces per 1,000 square feet over the entire yard. Then water a full inch. Measure an inch using tuna or cat food cans. In a week water another inch. In two weeks, repeat the shampoo and another inch of water. The shampoo will allow the water to penetrate the soil and set up a good environment for the soil microbes. They will fully recover over the winter assuming you get some rain or snow melt. Also you need to fertilize. I'm going to suggest using alfalfa pellets (rabbit chow) from your local feed store. Apply at a rate of 10 pounds per 1,000 square feet. Moisten them after you apply and the next day, drag a broom or hose around to knock the pellets down into the soil. Your new soil microbes will digest the alfalfa and restore your entire microbial system. They will also feed your grass as a byproduct of their food chain. Continue watering deeply on a weekly basis unless your soil gets soggy. Then back way off on frequency. The soil should not be soft longer than 3 days after you water. After a month, no matter what your weather, apply alfalfa but at a rate of 20 pounds per 1,000 square feet. This is the normal dose, but the first time you did not have enough microbes to properly digest it. Had you applied at 20 pounds then, you would get a sour ammonia smell. And I would repeat the alfalfa monthly as long as your bank account holds out...or until the grass stops growing.

And now that I've written all that, it occurs to me that I've wasted my time, because you're still not going to water or fertilize next summer. But if you did, your lawn would be as nice as your neighbor's lawn by May.

Stay away from weed-n-feed products. If you need fertilizer, use fertilizer. If you need a herbicide, get a liquid that you can control and just spot spray (mist) the leaves of the weeds you want to kill.

I would not core aerate or seed this year. The shampoo will soften the soil for you. I'm counting on the existing grass coming back to save the day for you. Really all it needs is water, mowing relatively high, and fertilizer.

What's ed's problem?

Most lawn advice IS generic. That's because growing one kind of grass is often much like growing another kind of grass. I know that because I've been moderating three different lawn forums for 10, 10 and 5 years. (this forum has no moderator so don't blame me for anything that might happen) The best practices for lawn care are listed above in my previous reply. If you don't want to do them, certainly nobody is going to come through your computer screen and grab you by the throat, but they are at least worth a try? Why? Because they are free! You have to water, mow, and fertilize anyway, so you may as well do it according to the ways that have proved to be successful.

I try to adjust the advice according to the needs of the OP. If he has a great lawn and wants to have the lawn of the month, I know how to help him. If he has dirt, I know how to help with that, too. If he just wants some thing green and doesn't care what it is, I can help. If he wants specific advice on which seed to get, I will not help with that. First of all I don't care about those details, and secondly, it would take me as much time to figure it out as it would anyone else. But that's just generic ol' me.