Cleaning:
Don't use steel wool or copper wool. It will scratch the surface and cause sticking.
Use Barkeeper's Friend powder.

Alternatively, you can try soaking the pan in vinegar, then clean as usual with a mild detergent and soft cloth.

Seasoning - Avoid Sticking:

  1. On medium to medium high heat, heat your pan for 2-3 minutes.
  2. Take it off the heat and melt a little coconut oil or other high heat oil in your pan and swirl the oil around to evenly coat the pan.
  3. Put it back on the heat and allow the oil to smoke. Once the oil has smoked, turn off your burner and remove pan from heat source and allow to cool completely. You know your pan is seasoned and ready if you can see your reflection in the pan

    Wax for wheels (split rim ) Shinneyness depends on the TYPE of stainless steel the manufacturer used to make the pan. If they used 18/10 or 18/8 steel, the surface can be shiny. If they used 18/0 steel it will be satiny. This is because of the metals used. The 18 is the percentage of Chromium in the steel. The 10, 8 or 0 is the percentage of Nickel in the steel. Nickel creates the shininess.

  4. Once the pan has cooled, pour out the oil and wipe the pan out with a paper towel. You now have a seasoned nonstick stainless steel pan.
You can cook like you would with a non-stick coated pan.
No oil, don't wash, just wipe clean.
For eggs preheat your pan on medium low heat for 2 minutes then put the eggs in.
Even well seasoned pans will need extra oil for higher temperature cooking..
Source: How To Cook On & Season A Stainless Steel Pan To Create A Non Stick Surface! | WholeLifestyleNutrition.com

Links:
Why no steel wool?
3 Ways to Clean Stainless Steel Cookware - wikiHow
How to Keep Food From Sticking | The SweetHome
last updated 24 Apr 2017