How do I get rid of quackgrass?

There are no known effective means. The problem is quackgrass is a grass plant species just like the Kentucky bluegrass that makes up most of your lawn. 

All species of grasses have common hormones and process their food almost identically. Therefore any type of herbicide or other chemical control will also kill the Kentucky bluegrass that you’re trying to keep.  

Why not just dig it up? Because this is the worst thing you could do! Quackgrass has incredibly extensive roots. Dig it up, and you’ll never be able to get all of the roots out. In fact, the roots that are left in the soil will sprout new quackgrass plants in greater numbers than you had before.

So all you can do to keep quackgrass in check is to keep your lawn mowed often. Quackgrass is a voracious grass. It grows very rapidly. It has a very large blade, which it needs to photosynthesize enough food to support that large root system. 

Keeping your lawn cut often will limit the length and size of the quackgrass blade, stunting the extent to which the plant can develop and spread.