Soap scum tends to build up on marble showers, so it's best not to go too long between cleanings. If you can, wipe the shower down with a squeegee after each use; if that's not realistic, at least try to do it once a week. If you notice that the shampoo or soap you use is leaving large deposits, you may want to switch to a different product so that you do not have to remove residue so often.
Because of the chemical makeup of marble, many common products for shower cleaning that are sold in department stores will damage it. Make sure that whatever product you use is specifically formulated for use on stone, or that the package at least says that the product is stone-safe. Because marble is sensitive to acid, avoid common household cleaning and disinfecting agents such as vinegar. Instead, clean off stains and scum with bleach, ammonia, acetone or hydrogen peroxide. Never mix chemicals when you clean your marble.
Use a bathtub or shower mat to protect the bottom of the shower. Marble can scratch easily, so in the event that you drop the shampoo or your favorite back scrubber, it's good to have the shower mat take the hit instead of your marble.
If your marble shower gets water spots or minor scratches, you can buff them away with a little 00-grade steel wool. If the idea of using steel wool makes you nervous, you often can find hard plastic-based scouring pads designed for the same purpose as steel wool. The advantage of using the plastic pads is that they will not rust like steel wool can.
One of the best things you can do for your marble shower is to put a layer of sealer on it, if it hasn't been done already by the manufacturer. The sealant protects the marble from minor abrasions and ensures that you'll be rubbing against the sealant rather than the actual marble when you clean. It also prevents water from seeping into grout areas and gradually wearing away the marble.
Don't run the water at extremes in temperature. If you run a shower that is excessively cold or hot, the temperature shift can cause the marble to crack. Aim for showers that are just more than lukewarm rather than steamy hot, and if you have to change water temperature, shift it gradually rather than all at once.