I have seasoned a lot of cast iron skillets over the years.
There is no "quick" method
per se.
First off, yes, in the oven, do the peanut (or better yet, canola) oil as a start as Aggie suggests. Do it as many times as you are patient to do. But do it in iterations - you want to build a basic "foundation" of layers.
But then, use it two or three times to cook bacon at a very low heat - I'm talking making your bacon slow cook very slowly - like taking a half an hour at the lowest heat setting possible (I love our newest stove because it fires at the high heat and you can turn it all the way down and still have flame - why did it take the industry 100 years to figure this out?).
This will get you to the basic "seasoned" level.
An alternative (or additional) method is to do a very slow cook (or two or three etc.) of a very fatty cut of pork roast (e.g. butt or shoulder) on a rack that fits inside your skillet such that the fat drips off and slowly bakes on.
Also critical is to NEVER, NEVER, NEVER scrub the pan such that you ruin the "patina" you are constucting.
Once it is truly "seasoned" a cast iron pan will rarely require anything more than a quick sponge cleaning. You should not have to "scrub" it with a metal pad etc. except because of some kind of cooking error.
Oh, and I always dry wipe my cast iron so that they do not "air dry" (rust is your constant enemy with cast iron - particularly if it is not fully seasoned). Also, you should hand clean it - sorry, no dishwasher for my cast iron!
My favorite cast iron skillet is probably almost 60 years old. I got it from my parents when they were clearing house for retirement some 25 years ago. They first seasoned it after they go married in 1948.
It is my "hallmark" cast iron skillet to which all of the others (skillets and dutch ovens etc.) I've acquired seek to emulate.
Remember this, no cast iron cookware is ever fully "seasoned" - it is a lifetime endeavor (and beyond that because they never wear out!).
Go to tag sales and flea markets and buy someone's (non rusty) discards if you can. Because, quick seasoning aside, it takes years to make a cast iron skillet a REAL cast iron skillet!
Oh, and I do not believe that you can effectively truly season one of those skillets that have the grooves built in to make nice marks on hamburgers! Stupid gimmick to my way of thinking. But, BTW, slow frying fatty burgers will always add "seasoning" to your skillet.
The best old cast iron skillets were made by
Warner in Sidney, New York. They went out of business a while ago.
Old Forge in Indiana makes the best ones I've found lately. There may be some good ones coming out of India and China now - so long as they are heavy gauge.
As you might have gathered, I am a cast iron cookware afficiando!