A lot can be gained by being a bit methodical about tasting wine. It will force you to examine the structure and complexity of a wine, rather than just one aspect of it. It is important to look first at the colour of a wine, then to smell it carefully, and only then to taste it. Even in the mouth it is a good idea to separate up the experience. A wine does not have a single taste, but is more like a journey, with a beginning, middle and a finish. And then there is the aftertaste.

Colour
This will tell you mostly about how developed the wine is, and also about its concentration. In a white wine paleness will indicate youth, often together with a greenish tint (also associated with cooler climate). A yellower colour may indicate warmer climate, more age and/or oxidation.
In a red wine try to judge how blue the colour is. Colour comes from the anthocyanins in the skin. These are predominantly blue but this blue colour is the least stable, the most easily oxidised and the first to precipitate out. A purple colour is the youngest and the wine will then tend to ruby, then mid red, then mature brick and orange tints. A very deep colour may well indicate concentration, ripeness, or a variety such as Cabernet or Syrah that has a greater natural quantity of anthocyanin.

Nose
Have a good sniff of the wine (easier in a glass that narrows towards the rim), possibly after giving the glass a good swirl. Try to pick out the fruit flavours, as well as anything else that comes to mind. This may well seem ridiculous at first, but anything that you notice here will help when it comes to tasting the wine. Obviously grapes when picked taste of grapes, but fermentation brings about amazing changes so that wine seems to taste of almost any fruit rather than grapes (well, Muscat still tastes grapey). Sauvignon can taste of gooseberry or elderflower, Cabernet of blackcurrant, Grenache of raspberry or plum, Pinot Noir of strawberry, Syrah of bell pepper, Sangiovese of blackberry, Vermentino of white peaches, and Gewurztraminer of cheap scent or lychee.
Then there are the flavours added by the winemaking. Sealed fermentation tanks can give rise to slightly confected or bubblegum flavours. Very low fermentation temperatures can result in banana or acetone/peardrop flavours. New oak casks or vats can give a sweet vanilla character, or in conjunction with say Chardonnay buttery or hazelnut aromas.

Palate
The mouth itself is a fairly crude tasting organ. It is sensitive to salty, sweet, sour, bitter, astringent and umami sensations through various receptors. The structure of the wine can be judged here and it is important to think about relative levels of sugar, acid, tannin and alcohol. Tannin in fact cannot be tasted but felt. Ripe tannin tends to form long chains that do not fit into the receptors but gives a feeling of body, while unripe tannin is shorter and will give the receptors a strong astringent feeling and possibly a green taste. Umami is a new discovery to the world, and finally seems to mean a strong taste of yummyness.

Try to think of tasting a wine as a long experience, not a static one. The initial impression is likey to be made by the fruit and sugar, if any, in the wine and the finish by the acidity, alcohol and tannin, again if any. The centre is where it all comes together and the fascination is the interplay.

Aftertaste
To some extent this is the opposite of the tasting experience as the tannin and acidity dominate at first, and the fruit will appear behind it. The persistence of the experience is important in evaluating the quality of the wine; the longer the better.

The more you concentrate on the taste of wine, the more taste you will slowly discover. As a consolation to those of us who lament our tasting abilities, life as a supertaster seems more problematic than pleasant. Sophisticated tastes are mutant tastes in that they go against the primitive warning signals about dangerous foods, but can deliver wonderful rewards. Supertasters however find it hard to go against the natural warnings of astringency and bitterness to which they are particularly susceptible and consequently find dry red or even dry white wine harder to enjoy.