This moving from a rental to owning a home and having lawn care is certainly a learning experience... We're working to have a lawn of St. Augustine grass here in Southwest Florida. I've successfully helped out an area using plugs, but have much of the yard (probably around 40%) with areas where there grow up a few days after cutting. Are these weeds or a type of grass? I tried uploading an image to Google Image search but didn't get any help. Thanks!
Sedge or more commonly known around here as Sawgrass for the nasty cuts you can get off the leaves.
It's found in swamps and overly wet areas in your lawn.
Catch the seed heads before they mature.