Should I season a Teflon-coated stainless steel frying pan

You've got a great pan and in a short time I'm sure you'll come to love it.

When using a standard pan (one without non-stick coating), heat your pan dry over high heat until you can hold your hand about 6-inches above the cooking surface and feel the heat radiating upward. This allows the tiny cracks and crevices that are imperceptible to the bare hand to expand and when the oil is added, it will coat and create a more even cooking surface.

Add just enough oil to lightly coat the surface. Adding to much oil leads to pan-frying which is fine if you're frying chicken but not what you want when searing and sauteing meat. There should just be a thin film across the bottom of the pan. An additional benefit to first heating the pan is the fact that it will actually take less oil to coat the pan due to the decreased viscosity. When the oil hits the hot pan it will instantly heat and should shimmer across the bottom like water on a freshly cleaned windshield.

You don't put the oil in the pan first because the longer oils and fats heat the quicker they break down and smoke. If you were to add cold oil and cold food to a cold pan and then start heating, you just end up with a big sticky mess.

Make sure you're prepared to add the food to the pan once the oil goes in otherwise the oil will start to burn.

The issue with burning and overcooking is going to be a matter of controlling the heat. Start searing and sauteeing over high heat because as food is added it will suck a good deal of heat from the pan. If it isn't extremely hot to begin with you'll end up with a steaming mess of gray colored meat or vegetables that aren't doing much cooking. Once the meat is browned but needs further cooking you can always turn down the heat to prevent excessive browning and crusting before the interior is done.

Even if you aren't planning to do a pan sauce, or if you've burnt what was cooking in the pan, you'll still want to deglaze with some water while the pan is hot (you can reheat it if it has already cooled down) so that you can scraped up the cooked on bits more easily and have less scrubbing to do when cleaning the pan.

I've never heard of doing anything other than giving it a good cleaning, as you would with any new item before first use.

I've only heard of seasoning used for cast iron and carbon steel, not for stainless steel. Looking online, I did find instructions for seasoning stainless steel, but I'd be inclined to look at the paperwork that came with the pan -- if the manufacturer recommends doing something, follow their instructions. If they don't, just give it a good wash.