this is the part of the yard I want to start with

dirt spot

here's some of the greener stuff up close

P.S. If anybody is considering getting a Monkey Ear Tree, DO NOT DO IT!!!! I hate that darn tree. lol

1. 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 every 5 days 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.

2. 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.

3. 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. With chemical fertilizers, too little is better than too much. With organic fertilizers, too much is better than too little. 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.

Great photos, by the way. Very helpful to assess your situation. Stay far away from weed n feed products. They do not work like you think they would. If you seriously want to spray something on the weeds, first determine if you have any St Augustine grass. You probably do and you really should target St Aug as your future lawn. But it does not respond well to "normal" herbicides. There is a special spray herbicide you can use for "southern lawns," a euphemism for St Augustine. Watch for it. I believe it comes in a black bottle with a purple label from Weed-B-Gone. Then spot spray your weeds rather than spraying the entire lawn. But don't spray right away. Fertilize the area first. Then about 2 weeks later, when the weeds are under the influence of the fertilizer, then spray them. Weeds die best when they are fairly healthy.

If you want to go with organic fertilizer you can start applying any time you want. I would suggest starting with something easy to find like rabbit food from your nearest feed store. It comes in 50-pound bags for about $10. Apply at a rate of 20 pounds per 1,000 square feet and moisten it after applying. Rabbit food is pelletized alfalfa. By moistening it the water will soak in and break the bonds of the pellet. This makes it impossible for birds to come in and eat all your fertilizer. Even though you would be applying rabbit food to the lawn, you will not see an increase in vermin. It gets moldy quickly and the mammals won't touch it. The mold is good, by the way. That's what you're looking for.

The dead areas are near the concrete. Concrete absorbs heat all day and releases it at night. Consequently your soil dries out much more thoroughly near the sidewalk and driveway than in the middle of the lawn. You might consider planting a shade producing shrub in the corners where the concrete provides heat from two directions.

In relooking at your pictures, you really need to reset your mower to the highest setting. It will take several weeks of growing for all the grass to get up to 4 inches high so you won't be mowing much until it gets up there. Let it go and grow. Tall grass will solve most of your weed problems and give you a very plush look and feel.

St Aug spreads very well when it is moist and fertilized. Some people believe it spreads faster when mowed lower but that has not been my experience. Keeping it moist is something you might just want to wait for (rain). Over fertilizing with organic fertilizer is what makes it spread best. Last year I applied 20 pounds per 1,000 of corn gluten meal every month. My lawn never looked that good!! It was apparently underfed in years past. You can't do that with chemical fertilizers without problems but you (almost) cannot overapply organic feeds.

Yes, rake out the duff. That will help it spread. Compost the leaves and use them somewhere.