What’s the best way to fix a broken kitchen drawer?

First take the drawer out and work out what actually failed: the front may have separated from the sides, a corner joint may have opened, or the bottom may have slipped out of its groove. Those need slightly different fixes.

For a wooden joint that fits back together closely, clean off loose old glue, apply wood glue to the mating surfaces, then clamp it square while it dries. Glue won’t make a wide gap strong, so don’t count on it to fill missing material.

If it’s a drawer front coming away from particleboard sides, a couple of small corner brackets can help hold it in place. Refit the front carefully, drill pilot holes, and use short screws so they don’t poke through the face or sides. Scrape away loose residue first and clamp or otherwise hold the front aligned while the adhesive cures.

Check the bracket screws against the actual thickness of the drawer. A screw that seems small can still go right through particleboard.

Don’t buy parts until you’ve checked the bottom and the runners too. If the bottom has simply slid out of its groove, putting brackets on the corners won’t solve that. If the drawer is badly crumbled where the screws or joints need to hold, replacing that piece may be more reliable than adding more adhesive.

For a first repair, take a few photos after removing the drawer and note which surfaces meet. That makes it much easier to choose a fix without forcing the wrong joint together.