This section is under-construction but already contains useful information.
I've been pretty disappointed with most of the pans I've used over the years, which also came with not knowing how these are properly used. Here is quick summary of that.
Some of the pans I've used have next to the casual teflon layer which you are probably familiar with some other materials called often something with "Permanent" or "Perm" in their name. They are okay but work in my experiences only for really really low heat stuff, good for warming vegetables but really pan frying takes a toll on their coating so i tried to avoid that. They are great though if you wanna crisp up stuff like rice because the heat required is not that great but it comes off without effort.
Probably my favorite way to cook, quick to heat up, takes high temperatures well. But it has to be used correctly. other wise you will spend more time cleaning and abandon your loved ones. I'm not an expert, you can find on youtube actual chefs recommending the optimal usage look up their videos if you want more in-depth. Most importantly for me; get the hot, then add oil swirl around so everything is coated, if the temperature is right you can see some convection in the oil as it heats up. You can also test this with a drop of water the drop should be able to freely float around on top of a steam bubble beneath it. It's quite fun to play around with this when you first get a stainless steel pan so definitely try it out to get familiar with it.
But no matter how well you cook you probably will have some bits stuck to the pan, for vegetables and such I like to add a tbsp of Sake at the end for nice flavour and cleaning of the pan as acidic liquids allow you to get rid of all bits from the pan surface. You can also make an amazing sauce from these bits, best for example in french cuisine with a bit of wine and then reduce in thepan. When your not in the mood for this, just pour in a good amount of water and let it simmer until all the flakes from the pan have been loosened.
Probably the best tip I can give for occassional cleaning of some burned in bits or discoloration after it has been cleaned is to make a classical italian tomato sauce in it. Short: Fry Sofrito, add some red wine, add a can or two of finely chopped tomatoes, reduce.