I've been drinking tea and pondering over each one for about 2 years now, and I've improved a lot since I started. Consequently, I see a lot of blank stares when most of my friends (besides my high school pals) listen to my musings on what I find during our tea sessions. So I guess it's as good a time as any to explain how it works for me (because who cares about university assessments, right?).
Appreciating tea is a very personal pastime, and for me it's probably the most time-consuming of my hobbies besides drawing. It's a very routine part of my life, and now that my parents have stopped complaining about the unfounded deleterious effects of drinking tea, I've been free to do so several times a week. I think it could even be called a ritual.
I find it to be incredibly rewarding, and well worth the money I spend. There's just so much joy to be found in a small cup of tea... Gosh that makes me feel a bit old. Hmm...
So anyway! The first thing you need to know is that this sort of thing takes time, concentration and persistence. This is probably best done on the weekend. Otherwise, you can just brew whatever and drink mindlessly on a busy weekday. Fortunately, getting started is easy!
Step One: Get out there and try all sorts of food!
Being aware of the sensation, savouring the food and remembering what you felt is the only way you'll recognise the interesting notes in the tea afterwards. I cannot stress this enough, as your tea time will only be as good as the effort you put into exploring culinary delights. Take it as another opportunity to hone your focus with something less challenging.
Step Two: Take the plunge...
The second step, which is a bit harder, is finding that first note to add to your olfactory library/record. This also holds true for alcoholic drinks (none of that cocktail nonsense). For whiskey/scotch/rum, the easiest one is vanilla (due to the barrels they use). For tea... That depends on the type of tea you're drinking. Black teas have a stronger malty taste, while green teas are more delicate and floral.
The best analogy I can come up with is... a puzzle. Each one is a different puzzle, but they have pieces that can be used in other puzzles. Once you "unlock" a piece of a puzzle, you will most likely be able to use it elsewhere. Sounds a bit like an RPG... It seems a bit intimidating, but the key thing to remember is that once you have found something you can recognise, that will draw you into the experience, help you train your focus and find new things.
Once you make that leap, it becomes way less mysterious. Then you will be able to put the first one to the back of your mind and sift through the rest of the sensory feedback. Once you start taking parts out of the "cloud of mystery" it shrinks and everything becomes clearer... What was once formless takes shape and can be comprehended. It gets easier with time and practise.
One last thing (which is probably the biggest misconception when it comes to appreciating tea or alcohol) is that you don't always really taste XYZ in many cases. Well, you don't taste it fully as though it were added to the drink. Usually it's a lot more subtle. For example, if I were to say there was passionfruit in one of my teas, it wouldn't be like I was actually eating passionfruit.
There are also cases where certain sensations remind you of something you've eaten. I recall one tea that I was enjoying at my friend's home. The tea was intriguing... It didn't exactly taste like peach, but there was some sort of flavour there that reminded me of an indescribable quality unique to peaches. To be honest, even my pal Peter did not know what I was talking about. Which brings me to my final point...
A lot of this is really subjective. What you pick up from a cup of tea may not match up with what someone else can detect. Because of the aforementioned first step, your time spend outside of tea will colour what you can taste and enjoy. But sometimes I don't think it matters if no one else can sense what you do. That just gives you special moments where you can enjoy a truly unique and personal experience.