For over 2,000 years, every class of Japanese society has enjoyed sake. Increasing in popularity around the world, sake is an alcoholic beverage that is often called "rice wine", but whose fermentation process more closely resembles the production of beer. Truly, many feel it should be classified on its own, clearly distinct from wine or beer.
The principle ingredients of sake are rice, yeast, and natural spring water. The finest sake is made only from the central part of the rice grain.
Pictured below is a chart of sake levels increasing, from bottom to top, in quality, price, fragrance, complexity, and the degree to which the rice grains are polished in the milling process.
The most common, regular sake is akin to "table wine" and is an everyday favorite. Junmai (means "pure rice", rice grains milled to at least 70%) sake is step above regular sake and is brewed without any additional alcohol or spirits. It is more acidic-sour and tangy, has more body, etc. Ginjo sake is more finely milled to at least 60% and fermented for longer periods in colder temperatures. In some cases, pure distilled alcohol may be added--producing a more refined, fruity, complex bouquet. Dai-Ginjo sake is a sub-classification of Ginjo. At least 50% of each grain of rice is polished and is handled with great care. Dai-Ginjo tends to be fruitier, lighter in body, and more fragrant. Junmai Dai-Ginjo is top of the line, premium sake made with very finely polished rice grains (Koji) and is produced in small batches using only traditional, hand-crafted methods. There are many other types of sake (Hon-Jyo-Zo-Shu, Nama-Sake, Gen-shu, Nigori, etc.) that are brewed differently and/or feature other additives.
Usually served in a traditional ceramic cup specifically made for sake (the ochoko), connoisseurs of sake may use different vessels such as various wine glasses to better enjoy sakes of differing aromas and intensity. Heating sake enhances the notes on the palate, but serving temperature varies according to sake quality and personal preference--though higher quality sake is usually served at a lower/cooler temperature.
When tasting sake, your approach should be similar to wine tasting. To appreciate the unique characteristics of sake, you should evaluate fragrance, acidity, earthiness, etc.