Remove the contents from the shelf you are moving or removing. As a precaution, it is also a good idea to remove the contents from shelves above and below the one being worked on, to avoid damaging something should you lose your grip on the shelf.
Look under the shelf where it meets the adjustable shelf clips. Some shelf clips secure to the shelf with screws; others attach permanently to the shelf. Grab the shelf at both ends with your hand and lift up. If the shelf clips come up with the shelf, lift the back of the shelf to unhook it from the wall. Pull the shelf with the clips away from the wall or cabinet.
Lift the shelf and slide it away from the wall and shelf clips, if the clips do not attach permanently to the shelf.
Inspect the clip holes above or below where the existing shelf clip attaches. If the hole is straight, the shelf clip simply pulls out. Some holes are slots with a cavity within the wall or cabinet under the hole. Grasp the adjustable shelf clip and pull up to unhook the clip from the wall or cabinet.
Squeeze the top and bottom of the shelf clip together, if the clip resembles a "V." This type of clip has flanges that secure at the top and bottom. Pull the clip away from the wall or cabinet, while squeezing it together with your fingers.