Kitchen drawers take a lot of abuse because they're opened and slammed closed all day long, every day of the week. Before you even notice, the knobs are falling off, or the drawer sticks or pulls to the side, or the bottom is coming out. As a structure, a kitchen drawer is fairly simple, and while glitches are annoying, in the end, there are a limited number of problems that can affect it. A quick examination of the drawer in question will tell you if the problem is in the mechanical works or with the drawer itself.
Pull it out as far as it will extend. Listen for clicking noises when you open or close the drawer to identify loose screws.
Lift it up and out of the frame. If the drawer will not open or lift out easily, look inside to see if utensils or other objects are stuck and jamming the works. Tighten the screws or replace them if you heard rattling in the works.
Empty the drawer and release any wedged objects if you have not already taken the box from the frame. Otherwise, take it out after it's been unstuck and wipe it out with a damp cloth. Be prepared to redistribute some of the contents to other places if the space is just overly full.
Reinstall the drawer straight on its sliding tracks if it was moving at an angle when you tried to pull it open. Wiggle it gently into place if necessary. Spray it with a small amount of WD-40 if it just seems to drag a little bit.
Measure the inside floor of the box. Measure and cut out a new panel of the same size from an appropriate wood and press it into place to assist a saggy bottom or to help square a twisted frame.
Examine the condition of the wood in case it has cracked or broken, or if the original glue is old and dried. Scrape out any old glue that is barely holding parts together.
Insert new wood glue in the area in question and apply pressure to hold the drawer together while it dries. Brace tricky areas by tying them together with bungee cords or even clothesline. Set the drawer to dry completely before trying to use it again.
Overloading a drawer can be the cause of many problems.