You may be tempted to use the scratchy side of your sponge when you're cleaning the shower doors just to get that extra oomph to get up the hazy residue. Don't. Do. It. Most shower door glass has a plastic coating on it to keep the water from sticking as much to the surface. That scrubby side of the sponge will scratch it and make it look mottled after awhile. Rely on the (green) chemicals to do the heavy lifting (see previous post).
Mostly I've found that shower glass cleans up well with an all purpose cleaner. I use the 7th Generation brand. But after awhile, near the bottom of the inside of the glass, you often find a hazy build-up that's hard to remove. One product that does this great is Ecover Bathroom Cleaner. I highly recommend it, though it's hard to find now so you have to look for it online and be persistent.
Ecloth is the maker of specialized microfiber cloths. You can find them sold in many supermarkets.They make a large assortment but I have found a few to be essential. Today I'll talk about the "cleaning up pad." This is essentially a sponge, but better. It has a smooth side and a rough side (though not as rough as a green scrubbie) and holds dampness like a sponge. But it cleans much more thoroughly than a sponge (as all microfiber cloths do) both in the dirt and grease it "grips" and in the amount of germs it removes. Highly recommended. www.ecloth.com
.Do what the pros do when you clean your house: wear a cleaning apron. it has pockets to put cloths and loops to hang products from. That way everything is with you as you make your way through the house. Saves time! A good one can be gotten at www.thecleanteam.com.