re: My lawn from hell. How do I fix this?

That yard doesnt look too bad. The first thing you need to do is have patience. That wont clear up in 6 months. In fact it may take 2 more seasons. Do the post emergant per instructions on bag.

Next year, start early with pre-emergant and cut your grass weekly in Feb-March even if it doesnt look like you are cutting anything. This chops the early weed sprouts down, keeping weeds and undesirables from growing further and spreading or getting mature. Late spring, the grass will over take weeds.

Jan-March is when you prevent weeds for the entire season.