Crabgrass can be tough to eradicate. Its flat-spreading nature allows it to avoid your mower blades while effectively shading out your grass.
1.
Kill. Knock back the crabgrass/weeds now.
2.
Improve your soil by spreading organic fertilizer like Milorganite or compost, so it can work it's way into the soil over the winter. Reapply in early spring.
3. Early spring, while your lawn is still pretty bare, scratch the soil lightly and
reseed with Contractor's Mix grass seed. Time this according to local conditions.
4.
Let it grow tall at first to shade out remaining weeds.
Going forward, mow regularly, not too low, and reapply organic fertilizer twice a year. If your soil is compacted, these methods will actually "uncompact" it over time. In future, try to mow using lighter-weight equipment, and vary your mowing pattern. Take a "before" picture now, and another one next summer.
This is a proven, no-chemical, less work, method that I used when I was a landscaper to renovate many lawns.
Kill. Many will suggest drenching with Round-up. Even if you don't mind the chemicals, I find it not terribly effective as many weeds are pretty resistant now. Plus it is less effective out of the active growing season. I've found baking soda to be quite effective as a one-time kill that also spares what grass you have. No one ever believes this, but it actually works faster than Round-up. A light sprinkle is all you need. Try it on a small section and see if it works on your crabgrass. (There are a few species of weeds under the general rubric of "crabgrass".) This time of year, once you knock back the crabgrass it won't be able to regrow very well until spring. You will have bare patches but winter is around the corner when your lawn will be bare anyhow.
Improve. Your spring re-seeding will be much more successful if you've improved the soil over the winter via the organic compost. Even if you killed everything last fall, you have a lot weeds that will regrow from the roots, plus a zillion weed seeds ready to sprout come spring. Milorganite or compost will slowly decompose and work into the soil over the winter and will actually improve the structure and chemistry of your soil. Weeds will not like this; they grow best in poor, dry, compacted soil. Chemical fertilizer is a quick-shot that helps everything, including weeds, to grow and does nothing for your soil.
Reseed. The advantage of Contractor's Mix is it contains some fast-growing grasses such as rye, that will shade out spring weeds while your fescues get their act together. I find that fescues can never outcompete weeds; rye grasses can. (I know you wonder why the rye doesn't outcompete the fescue; not really sure, but it may be partly because weeds actually excrete chemicals that hinder grass growth.) All I know is, having tried every grass seed, it works the best.
Deeper plowing or turning of the ground will turn up a zillion new weed seeds ready to sprout in spring. With Contractor's Mix, a light scratch is all you need.
Going forward, try to prevent weeds from sprouting in gardens and beds, which will then try to spread to your lawn. You can apply corn meal (the active ingredient in "Preen" but much cheaper). Careful, it will keep your grass seed from germinating too. Mulch heavily; fill your beds thickly with plants that will shade out weeds.
Although I prefer not to use chemicals, my clients didn't care, but they did expect results. The worst lawns were always the ones where the folks used one of those lawn services, which basically consists of a big truck spraying chemicals on the lawn every other month.
