When a drawer won't pull out, the chances are that something inside is projecting above the sides. Simply remove the drawer above, then empty and repack the sticking drawer.
A loose nail in the drawer frame may also be the culprit; if so, hammer it down.
When the bottom of a wooden drawer sags, turn over the drawer. If nails hold the bottom to the back, pull them out with pincers. Break the glue blocks from the bottom with a chisel and mallet. Slide out the bottom and turn it upside-down. Then re-nail the bottom to the back and glue the blocks back in place.
If the sagging bottom fits into a groove in the back of the drawer, you must dismantle the frame to fix it. Wrap a cloth around a mallet and tap apart the dovetail joints at the corners of the drawer. Slide the bottom out, scrape off the old glue, and reassemble the drawer with the bottom upside-down.
Replace a split bottom with thin plywood, or mend it with a canvas strip and pva adhesive.
If a wooden drawer drags, sand its runners lightly and then rub them with a candle stub or a bar of soap, or dust with French chalk. Or if the wood has swollen in damp weather, lightly sand or plane the front lip of the drawer and along the tops of the sides and back.
If a wooden drawer pulls out too far, the chances are that you need to re-attach or replace either the glue blocks that secure the drawer bottom, or the stop that is on top of the rail-below the drawer at the front of the chest.