if you can't keep up with cutting it out and it has taken over most of the lawn.
1. You can use a non selective herbicide to make sure you kill the roots. It will kill the grass around it then you can dig out and patch the lawn. You need to kill the roots and the runners and digging them out alone may not get all the roots or stolons of the perennial grasses.
2. Perennial grasses are harder to get rid of than annual ones.
3. If there are more weeds than lawn it would be costly but the easiest way to do it is to kill everything off. Re amend and then water and roundup to make sure nothing more pops up before replanting.
4. Sometimes ou have to choose the grass that works best for the site and not the grass you like. Healthy turf will crowd out weeds better and some grasses are better at competing with weeds.
5 You have to get ahead of the weeds before they get established and mow at the proper height. Keeping the grass taller helps to compete.