There are simple solutions to the problem of how to fix a sticky drawer. Drawers become stuck for three typical reasons: mechanical, structural, and obstructional.
Check the easiest solution first by pulling out the entire drawer and look to see if there is any object in the way that might hamper the drawer's movement. Look both inside the drawer, above and below it, and check the sliders or tracks that the drawer rolls on to make sure there are no obstructions. If there is dirt or other tiny debris, dampen a cloth with water and wipe clean.
Make sure all the drawer mechanisms are tightly in place. Screws can become loose over time. Rollers and slides can break. If the drawer was forced to bear too much weight, the center can become bowed. Check both the drawer mechanisms and all the parts where the drawer is housed. Replace any screws (slightly larger ones will do), tighten anchors, add new nails, staples, or brads if needed, or replace any broken parts. Drawer guides and slides are available at home repair stores.
Once everything is mechanically sound, apply a lubricant to prevent friction and to help the drawer continue to not stick. A minimal amount will suffice. For wooden drawers that slide with no plastic or metal assembly, check for shiny spots on the underside of the drawer and on the place where it slides. They indicate where lubricant is most needed. Floor wax, the side of a candle preferably made from natural bee's wax, paraffin used in canning, or as a last resort a bar of soap with no skin moisturizing additives are good lubricants. For drawers with metal mechanisms, use a water displacement lubricant spray, and for plastic housings use a Teflon-based spray. Oil-based lubricants also work well for plastic and metal.
Sometimes, wooden drawers will stick due to expansion of the wood caused by the weather. In such cases, use sand paper to shave the drawer down to size. Do these steps if all else fails, and do it slowly, checking frequently to make sure the whittled-down size is correct. You can prevent this from happening again by sealing both the wood of the drawer and the cabinet with a coating of polyurethane or paint.
Drawers that do not move properly are an annoyance. But by following the above steps you know how to fix a sticky drawer with ease.