When I think of 
Sukiyaki, it conjures up two unrelated memories in my mind. One is a Japanese popular song called "Ue-o muite arukou" "
上を向いて歩こう"; translated into English, as "Let me gaze up while I am walking (and holding back my tears)". This was sung by 
Kyu Sakamoto 坂本九, who was later killed in 
a tragic commercial airplane crash in 1985. This is a melancholic song without any reference to food but, for some reason, was named "
sukiyaki"  when it was introduced to the U.S. The lyrics of the song and this  English title have absolutely no relation to each other whatsoever  except that both were from Japan--it is the equivalent to introducing "
Moon River" as "
Beef Stew".) Despite this, it was reportedly #1 on the Billboard magazine hit chart in June 15 of 1963.
Sukiyaki  also reminds me of the very first time my wife and I visited Kyoto  together so many years ago. Although we had visited Japan frequently we  usually headed straight to Hokkaido occasionally staying only a few days  in Tokyo. So the Japan my wife knew consisted of only Tokyo, Sapporo  and other parts of Hokkaido. For her, Kyoto was an eye-opening  experience--until then she thought all of Japan was like Hokkaido and  was surprised to see how different it was. 
 
On that trip,  one evening, we stolled along a narrow and crooked alleyway in Pontocho  先斗町. Since I did not do good research ahead of time (this was a time way  before internet 
Tabelog and  food blogs), we did not have any idea which restaurant we should try.  Then, I found what appeared to be an old Kyoto house with a small wooden  sign saying "Sukiyaki". Although it looked more like a residence than a  restaurant, I made an executive decision and we went in. As we said  "hello" or "konbanwa" at the small and deserted  "genkan" 玄関 entrance, a  kimono clad "nakai" san 仲居さん or waitress, came out from behind the  sliding "shoji" screen and greeted us. After removing our shoes, we were  ushered up into a large Japanese room (10 tatami-mat room or 十畳間)  upstairs which was just for us. We did not see any other customers and  the "nakai" san made conversations with my wife (through my translation)  and I while preparing sukiyaki at the table. It was such a different  and pleasant eating experience. The room was elegant in a slightly  shabby chic. It was so quiet and peaceful after the bustle on the  streets below. I do not remember exactly but it was not outrageously  expensive. (In later years, we visited Kyoto many more times. Every time  we visit Pontocho, we see that the stores in the alleys have changed  and new (chain?) restaurants and girly bars have started replacing old  traditional restaurants and drinking places. Although we tried, we were  not able to find our "sukiyaki" restaurant again. That meal turned out  to be one of those poignant but fleeting experiences--kinda like the  song. 
This  dish, sukiyaki, was invented after the Meiji restoration (1868) when  Japanese adapted to eating meat (beef) and also is one of the Japanese  foods accepted and popularized in the U.S. long before sushi and sashimi  became popular. Sukiyaki 鋤焼 (suki 
鋤  means a type of Japanese spades and "yaki" 焼き means to grill or cook.  But I am not sure that was how this dish was originally cooked.) has two  distinct styles; Kansai 関西 (includes Kyoto) and Kanto 関東 (Tokyo)  -styles. Mine must be a Hokkaido 北海道 style. Actually, when I was growing  up, my mother used to make sukiyaki with thinly sliced pork rather than  beef, which was (and maybe still is) common in Hokkaido.
We  have not made sukiyaki for ages but I found thinly sliced sukiyaki beef  (frozen), which was not as nicely marbled as Japanese beef, at a  Japanese grocery store and decided to make sukiyaki. Sukiyaki is  traditionally cooked at the table and "the man of the house" is  supposedly in charge of cooking and seasoning sukiyaki even though he  usually does not cook. A traditional sukiyaki pot or すき焼き鍋 is made of  cast iron、round and shallow with folding handles like one you see here. 
Ingredients: Besides thinly sliced beef, the most common items include tofu (especially grilled tofu or 焼き豆腐), Konnyaku thread or 
shirataki  (白滝) (boiled for few minutes in water and washed in cold running water  to remove its distinctive (read:awful) smell, shiitake mushroom (I used  shimeji here), onion (either regular, thinly sliced, or Japanese "
negi"  scallion cut in 1-2 inch long on a slant), some type of greens such as  spinach (I used a mixture of spinach and arugula here, which were very  briefly blanched). My wife likes the more traditional edible  chrysanthemum or 
shungiku (春菊)*. As seen on the left in the image below, I arranged the ingredients on a large plate before starting.
(*We  love shungiku for its distinctive taste and even tried to grow it  without much success. You could occasionally get it fresh at the  Japanese grocery store but the availability is sporadic at best.)
Seasonings:  You should have your seasonings handy while cooking sukiyaki; soy  sauce, sugar, and sake. I do not use a premixed seasoning liquid or  warishita 割り下. Just add these seasonings as you add more ingredients;  sprinkle sugar, splash soy sauce and then sake. Since this is done by  the man of the house, he does not measure anything (right, image above).
Cooking:   We did not cook the sukiyaki at the table this time. I placed a  sukiyaki pot on the stove on medium low heat. I first melted a bit of  butter (or you could use a chunk of beef fat) and spread the beef over  the butter. The proper and traditional way of serving sukiyaki, is to  season the meat after it has browned with sake, sugar and soy sauce.  Then all the diners taste a small portion of this first cooked meat,  since this is the only time browned meat was available to taste. (The  rest of the beef added later is just cooked in the seasoning liquid). I  do not see much advantage in this custom and I cooked everything  together as you see on the right in the picture above. The vegetable and  tofu exude water but if the liquid is not enough or the seasoning is  too strong you could add more sake or dashi. I put on the lid and cooked  it for 5 minutes or until the onion was done.
Serving:  The classic way is to serve a raw beaten egg in the bowl as a dipping  sauce (shown in the second picture above.) (of course, I used 
pasteurized shell eggs  for this). The egg will cool the suskiyaki and make it taste better for  sure. We just had this as a drinking snack rather than a meal with cold  sake. This is such a classic dish and even the inferior quality of the  beef did not detract.