Shower door handles can corrode, become loose, and generally need repair or replacement. Shower door handles are connected by screws and they are easy to fix.
Usually, the problem is that the handle is loose enough to the point where it either falls off or breaks off.
Shower doors either swing like a traditional door, or slide along a track.
Swinging doors have a small vertical handle that attaches with two screws. Sliding doors typically have a long handle that spans the width of the door. It will usually be held to the door frame by two screws on each side of the door. The most obvious fix is to tighten the screws to see if that fixes the problem. If the handles tighten back up, you are done.
If you need to replace the handles, you are likely not going to find them in a home center. You should try a glass shop. There are lots of different finishes on door frames. You can try your luck on the web, but by taking the part to an experienced glass shop, they will be able to get the exact part you need. In many cases you will have to order the parts, but getting the correct part will save you a lot of trouble.