In short, yes, you should season an un-coated cast-iron pan to protect it against rust and to prevent food sticking to the cooking surface.
This is something of a sacred process in places like the southern United States, where cast-iron skillets (pans to us) are used for steak with a reverent tradition.
You can season the pan once or several times if you want the oil baked deeply into the surface. It should not be sticky.
Wash the pan thoroughly (presuming you have 100% cast-iron with no wood handle).
Use hot soapy water and pot scrub.
Dry very well, leaving in a warm spot for a while.
Now take some vegetable oil on some kitchen paper and cover the pan and handle with a good rub — all over —inside and out, buffing off the excess.
It should look gorgeous already.
Pop it in a pre-heated oven at 375F/200C for about an hour.
Set up upside-down on a wire shelf, and leave a tray below to catch any drips.
Repeat oiling and baking three-four times, being careful not to burn yourself in the process!
Wash your seasoned pan after use carefully in warm soapy water without harsh chemicals.
Lightly oil before storing.