I have worked in two professsional kitchens. The main kitchen itself (all the work tables, stoves, floors, refrigerator fronts and so on) is cleaned after each service, and very thoroughly each night with hot soapy water and sometime sterilizing solution. The insides of refrigerators and other storage areas don't need to be cleaned that often because everything in them is in sealed containers. They should normally be emptied and wiped out at least once a week, and of course immediately if there is any kind of spill.
You could get yourself a specialized sieve brush - the things are meant for mining sieves but cooking sieves are generally the same size (0.5mm - 1.0mm, the latter being the no. 16 that the first link is talking about). I haven't seen any of these sitting in home kitchens - could be that they aren't effective on cooking sieves, but more likely, cooks just don't know or care that they exist.
For the truly dedicated, you could get yourself a studded sieve cleaner or the similar triangle kind with brushes. These are meant for cleaning really fine sieves, as in flour mill equipment, so whether or not it would be useful to you depends on what kind (mesh density) of sieve you have.
Or, if you could loads of money to blow, you could go all out and get yourself an ultrasonic sieve cleaner. Of course, we're now talking about products that don't even have a list price, so if you have to ask, you can't afford it.
Here's perhaps the most interesting option for those of you at home, though: I noticed companies out there selling rubber balls as sieve cleaners, so I was curious whether or not one could just use an ordinary rubber ball. I happened to have one of those big squishy stress-reliever balls sitting around and gave it a shot on my 8" sieve/strainer that had some sediment stuck on it - and guess what, it works! It's not perfect, it didn't get every last grain out, but I only had to rub the inside a couple of times with the ball to get out the vast majority of "dirt". So there's your "home remedy" for cooks on the cheap.
Best Answer
Run a clean plastic mesh covered sponge (we call them "dobies") under hot water and then squeeze out excess water so it is wet, but not dripping. Apply a few drops of dish soap to the sponge. Using a circular motion, wipe the counter surface to be cleaned, creating a light coating of thin suds on the entire counter. Take a dry dishtowel and remove the suds with long, even strokes that go from one edge to the other, pausing to refold the dishtowel so that a dry portion is always in contact with the counter, which will remove the suds effectively. Use a damp dishtowel to go over the surface again to remove any remaining soap. The counter will be shiny and streak free.