There is a saying in Hungarian that "Több nap, mint kolbász" (translation: "There are more days than types of sausage") meaning that you ought not indulge every day. For many, in fact most, Tokaji wines are approached only as a special treat; the common misconception that all Tokaji is sweet and all Tokaji is expensive. I, on the other hand, disagree. I think the wines of Tokaj are so varied and so well made that they can stand to be served with virtually any kind of food, in any ethnicity, on any day of the week.
In general, I prefer Tokaji chilled. Contrary to what some would tell you, the sweeter the wine, the less chilling it needs. The varietal Tokaji wine is quite refreshing and entirely more tasty at a very low temperature. Personally, I like it quite cold, or a temperature I would serve Champagne, at or around 43 degrees. The sweeter the wine, the warmer it can be served. I serve Aszú Eszencia at room temperature, 65 degrees.
Care should be taken when removing the capsule and cork. Tokaji (especially Aszú) corks are notoriously small. Those from the Communist era and before (even pre-1994!) can be less than half the length of typical cork and because of the narrow bottle neck, can be significantly smaller in diameter than a normal cork as well. The capsule is unusual in its size as well. Because of the "állami ellenőrzőjegy" or State Approval Stamp [This is the red, white and green band around the bottom of the capsule] the capsule should be removed as not to tare this band.
Virtually all Tokaji benefits from decanting. There are so many complex aromas in Tokaji wine that decanting helps even the mediocre wines to release their bouquets. For varietal wines, I open them at least 15 minutes prior to drinking and I remove them from the fridge or ice at that time. For Aszú wines, they should be decanted both to free themselves of a sometimes "gasoline" or "petrol" character that comes from bottle aging, as well as to release aromas and oxygenate them which "fleshes out" or loosens the sometimes viscus liquid into a more flowing, rounded character. I decant Aszú wines no fewer than 30 minutes before drinking and for Aszú Eszencia, 6 puttonyos, or an older vintage wine, as much as 2 days [!] in advance. Because Tokaji Aszú is already oxidized on the vine from Botryis, the wine in bottle cannot prematurely brown or "turn" as is sometimes know to happen in older Chardonnay or other white varietals.
Historically, Tokaji Aszú was stored STANDING UP. This required recorking at least every seven years as the corks would prematurely dry due to lack of contact with the wine. The reason for having the bottles stand up was that the wine would throw sediment (mostly tartaric acid, as well as must particulate) however the Tokaji Aszú being so thick with residual sugar would prevent the sediment from moving quickly to the side and to the bottom. The bottles too, were hand-blown and not uniform and did not store well on their sides. Bottles were stored upright giving the sediment the ability to collect at the bottom of the bottle preventing the sediment from redistributing while the wine was being served.
Today's more modern producers have eliminated the need for standing bottles upright by employing more careful filtering processes and more uniform bottle production. Recorking is almost unheard of today and with all of the home wine service gizmos, like decanters, coolers, chillers, filters, funnels, pourers, it simply isn't necessary or convenient to store them that way, never mind the recorking! Even at the wineries in Tokaj, new bottles are stored on their side. I store bottles on their side in order to keep the corks moist and to limit wine exposure to air. With bottles stood upright their is a greater surface to air ratio and in turn, encouraging evaporation.