At a quick glance I would say that over 50% of your lawn is not grass but a variety of well established weeds. This is at the stage where minor efforts are of no use. Even if you could magically remove the weeds other weeds would move in faster than the grass would grow in the summer. This detailed answer from Mike Perry may help you.
Some of the questions you have to answer first are:
- do you know much about the soil? get a pH test done and dig a hole to see how deep the topsoil is and whether it is clay or sand or junk.
- does it matter if it has weeds? You could just over seed with white clover and grass seed in the fall and not worry about it.
- is cost an issue? If not, then re sod. It's fast and produces results right away. You will need to water a lot if this is done in the summer.
- do you really need all of it to be perfect? Maybe there are some areas you want to look nice but the rest of it..... Then just re sod the critical areas.
Here are some of your options:
- fast and expensive is re sodding. Best time is the fall or spring.
- slow and cheaper is over seeding and topdressing with organic matter spring and fall. Every year you should see a small improvement.
- mowing and watering practices play a vital part in lawn health. Cut at least three inches high and water deeply and thoroughly in the summer months during dry conditions.