Skillets / Pans Stainless/copper vs cast iron | Caring for Stainless Steel pans | Protecting Stainless BBQs
 

First you should know that stainless steel usually contains some iron so will rust and it is not stainless.Stainless steel varies in quality, and manufacturers may use different grades for different parts of the grill.

Stainless Steel Cleaning - Weber Grills

How to Protect a Stainless Steel Grill from rusting | 9mmSteve
2 coats of car wax followed by olive oil.
You need to wipe most of the olive oil off or you will get brown spots where there is excessive oil.
Repeat a couple of times each year.

How to Prevent Rust on Your Grill Ghar-Broil

Stainless Steel Care and Cleaning
Spray a small amount of WD-40 or Sheila Shine on a piece of paper towel and rub with the grain over the surface of the appliance. Using a clean terry cloth or paper towel, polish the appliance .
Furniture polish, such as Old English, can be effective for polishing stainless steel and protecting the surface.

ProtectaClear Pint : Everbrite Coatings - Metal Restoration Products, How to Restore Metal, Protect Metal and Keep Metal Looking Its Best


Cleaning:
How to Clean a Grill - BBQ Cleaning Guide Cleaning:
How to Clean Stainless Steel Grill Grates
Mix 2 cups white vinegar to 1 cup of baking soda and pour the mixture directly over them. The mixture will foam instantly so work fast.
How to Clean a Stainless Steel Grill - Consumer Reports

Clean Your BBQ! - Clean My Space

If the grill is cast iron, you can use a wire BBQ brush (usually gold coloured bristles) and quickly clean the grates off using an up and down motion along the grill working your way from one side to the other.
If it is stainless steel or porcelain enameled or coated, use a stainless steel wire brush instead (usually silver coloured bristles). This is akin to using fine steel wool, it is very gentle and won’t scratch the grill.

Inside the lid:
remove the build-up regularly with a non-scratching brush (stainless steel), non-scratching scraper or non-scratching sponge. Once you’ve scraped everything off (and let it fall to the bottom of the cookbox), wash the interior lid with a soft sponge, warm soapy water, then rinse and buff dry with a soft cloth.

The Bottom of the Cookbox:
Remove as many components as you can, safely. Use a non-scratching scraper to remove any carbonized grease, build up or fallen food.
Many have pull-out trays that can be easily emptied into a garbage). This can be wiped clean occasionally as well, following the same protocol as above; clean with warm soapy water and a non-scratch sponge to remove grease, and boot up to a degreaser.

Tools:
fill your sink with warm water. Add a teaspoon of dish soap and a half cup of baking soda. Soak the tools or accessories and then scrub clean with a non-scratching sponge.


Links:
How to Clean a Stainless Steel Grill - Consumer Reports
How to Maintain Your Gas Grill - Consumer Reports
Cleaning your grill video | consumer reports