Ok, I bought this house and the lawn had been professional landscaped. I can't afford to do that, and with all the work I've been doing to the house, I can't find time to take care of it other than give it a mow when it needs. I also know NOTHING about landscaping or lawns.
Here are some pics. The lawn is being overtaken by weeds. Not shown int he pics are also 2 mulch beds I have with flowers that are taken over by weeds too. The lawn is 24,000 sqft and I have a full irrigation system running throughout as well as a ride-on lawn mower.
First you need to identify the type of grass you are dealing with.
Then start by fertilizing and watering then if you can pin point the weeds then apply herbicide, only one the gets rid of that weed not Round Up or Remuda, those will kill everything you spray it on.Or call a professional lawn care service, and have him or her explain what action they are going to take to kill the weeds, and take notes and DIY.
It also looks like you need to airiate and power rake to remove thatch
I can't tell from the picture if that is nut grass or crab grass or what it is. You might want to pull the entire weed including the root and take to your local hardware store and let them help you identify it to make sure you get the right herbicide.
Also, check your local Universities and see if they have an Agricultural Extension. They are a great resource and know the local weeds, grasses, etc., plus they offer free advice.