You can throw out a dresser.
In some locations a garbage collector will haul off the old dresser on garbage day if there garbage truck is equipped to haul off large items.
If not you can take the old dresser to a public dumpster or the landfill yourself if you have one nearby that allows the public to dump trash and other large items.
You can also set the dresser out on the curb and if your town or location has a bulky item pick up program available you can schedule your old dresser or other large items to be picked up.
If the dresser is in good condition you could even donate it to Goodwill or the Salvation Army or even set it out and someone may want the old dresser and may haul it off.