There are a variety of reasons why wooden drawers stick, or why they don't open and close as smoothly as they once did. One common reason is that over time, the wood dries out and becomes rough. When two rough wood surfaces rub together, friction causes the moving part to drag instead of gliding along. That's why wood drawers need to be lubricated from time to time to keep them working their best.
Remove the drawer from its cabinet by pulling it out. If it stops at the end, you may need to lift the front up to remove it from a catch.
Flip the wooden drawer over and set it on a hard work surface.
Clean any lubricant residue off both bottom edges and the centre guide of the drawer by wiping them with a rag. Remove existing caked-on lubricant by carefully scraping it off with a putty knife.
Clean any lubricant residue from inside the cabinet as well. Clean the edges that meet the edges of the drawer, and the centre guide.
Rub a block of beeswax in long, smooth strokes along the bottom edges of the drawer to lubricate the wood. Keep rubbing until there's a thin layer of wax on the wood. Lubricate the centre guide, too.
Replace the wood drawer in the cabinet. Slide it in and out several times to distribute the wax from the drawer to the wood inside the cabinet.
Beeswax works the best. But you can also use candle wax or bar soap to lubricate a wooden drawer. Apply wax to drawers at least once a year, if not every few months, to keep them moving smoothly.