For a quick inexpensive liner for dresser drawers buy a roll of heavy weight wrapping paper and use it to line the drawers.
Diy kitchen drawer liners.
It s easy enough to apply but nearly impossible to remove due to the super sticky adhesive on the back.
Many traditional drawer and shelf liners are made using contact paper.
I wanted a less permanent solution so i opted to use oilcloth for this project.
Glue down drawer liners are one solution but they re hard to remove and may reduce the value of your antique.