I tend to grab whatever is handy, usually just a damp rag. I also use an orange oil cleaner or a multi-surface cleaner. Pretty much anything works. I see no reason to use a specialty stone cleaner.

No special cleaners are needed. I use Windex, soap and water, just water, vinegar and water... whatever is handy.

You can use a special stone cleaner if you want, but it isn't necessary.

Here you go - Copied directly from the Silestone.com website:

Silestone Quartz Daily Cleaning Routine:

For Silestone Quartz with a polished finish, we recommend you use a mild household cleaner, such as 409®, Fantastik®, Lysol®, or Windex®. In case of stubborn spills or stains, soak the area for up to 10 minutes with one of the above cleaners and vigorously wipe away with a Scotch Brite® pad.

I usually just use water and a paper towel or cloth.

One of the managers of the Silestone and granite place that we got our Silestone counters from stopped by today to check up on how well we like our counters (we love them!). While he was here I asked him about caring for our counters. He suggested Windex, Formula 409, a mild soap and water or Simple Green (either the regular or the one specifically made for counters/stone). He uses the regular Simple Green on his own Silestone.
One thing he mentioned that I hadn't heard before was to keep hot cast iron pots, pans and skillets off the counters. Apparently, cast iron heats hotter and keeps the heat longer than most regular pans. The quick heat transference from pot to counter could potentially damage the counters, he said.

I've kept my Silestone and my Viatera counters clean with Method and with Simple Green, with the occasional boost from vinegar diluted a little with water. Washing off the vinegar immediately. I've been cooking here a little less than a year, though. But they look great.

Edit, I don't know that I have to wash off vinegar immediately... one reason I went with quartz over granite is that I cook a lot of acidic foods... call me a Sourpuss, eh? Quartz can deal with acid a lot better than granite... I just do it to be extra safe.

Silestone Eternal is especially prone to any alkaline cleaner, which is most off the shelf cleaners. It will remove the nboost coating leaving dull patches.

You need to follow the Care & Cleaning Essentials and nothing else. If you ring Cosentino they will tell you to use isopropyl alcohol though this is an electrical solvent and also affects the nboost coating.

The problem with a damp rag or soap and water it will leave the surface streaky.

The Method Daily Granite is fine to use, but it will not remove any stains.

Care & Cleaning Essential for Stone & Quartz