If you are inclined to go the chemical route Glyphosate is a non-selective herbicide for killing weeds and grass. "Roundup" is probably the best known brand name but there are other products. All the normal caveats apply- follow the label instructions and apply with care, etc. Being non-selective though it kills all grass and weeds so don't spill or drip. Since you're in the north it's likely all you'll need is one application. You will have to wait a few days for a good "kill" and will then need to do hand work to grade or rake out the dead grass. IMO this is the "easiest" but may not be the quickest- and some people are not comfortable with chemicals of any sort.
If you go this route big word of caution though. There may be some rule in your system about a time period between spraying of any kind and when kids are allowed back on the field. I've been told it's 60 days in our area.
If that's the case you're stuck with with the old ways- digging, raking, pulling etc. A small tractor, skid loader, or just a bunch of players with rakes and shovels can make quick work of smaller areas.
Overall this may be the quickest. Some places consider it a "team building" experience