The short answer
A label mainly reveals the origin, the producer or bottler, and the alcohol content. Depending on the wine, you'll also find the grape variety, vintage, and a sweetness indication. The largest print is rarely the most important piece of information.

What order to read things in
Take the bottle and read in a fixed order. First, the type of wine and the sweetness level. Then the grape variety and origin, if they're listed. The vintage comes after that. It helps you find a specific bottle again, and it's not a grade. Last, the name of the producer: you'll need that if you want to ask about the same wine later.
Big words are no guarantee. Reserve sounds like more, and a heavy bottle feels like more. What a term like that actually requires is set by the region of origin—the area the wine comes from. These rules differ from region to region. If you don't know them, it's better to ask than to guess.
The order has a simple reason. Type and sweetness decide first whether the bottle fits your occasion. A dry and a sweet wine from the same grape variety are two different drinks at the table. Grape variety and origin then narrow down the direction. Vintage and producer come last, since they mainly help with finding the wine again.
The largest text on the label is often just a name meant to sound appealing. The details you're actually looking for are usually printed smaller and less prominently. So make a point of reading the lines your eyes would otherwise skip. If a detail is missing entirely, that doesn't make the wine worse. Not every piece of information has to appear on every label.
What's often on the back label
On the back label, you'll often find a description in plain language. Along with that come notes on aging and details about the bottler. Aging means: how the wine matured after fermentation, for instance in an oak barrel or a steel tank. Words like fine or elegant, on the other hand, only become useful once you can match them to your own experience.
If you're saving a favorite bottle, photograph both sides. Note down where you bought or drank it. That way you'll find exactly this version again later, not just a similarly named one. This is especially useful when there are several wines from the same producer, since it prevents mix-ups.
The text on the back label largely comes from the producer or bottler themselves. What's useful about it are the verifiable parts: who bottled it and how the wine matured. Treat the flavor descriptions more like a prediction. Drink the wine, read the text again afterward, and check whether elegant matched what was actually in the glass.
When photographing, it's worth taking a little care so the small print stays legible. Tilt the bottle slightly so the flash doesn't reflect off the glass. Better to take one photo too many than one too few. A brief note on the date and occasion helps too. You'll remember the evening months later more easily than the name on the label.

Label details that often get misread
The most common misconception concerns the vintage. Many read it like a grade and look for the better year. On the label, it's simply a piece of information at first. It distinguishes one bottle from the next. It becomes important mainly on a second purchase. If two vintages of the same wine sit side by side on the shelf, the number tells you which one you already know.
The second misconception concerns presentation. Heavy glass, embossed paper, and the word Reserve together look very high-end. None of it is reliable. What a designation actually requires is regulated by the rules of the specific region of origin. Without that knowledge, the impression stays a guess—and guessing can cost you money.
How to apply this in the shop
Take the bottle in hand and turn it all the way around once. On the front, look for the type of wine and the sweetness indication. On the back, look for the bottler and the notes on aging. This takes less than a minute. It prevents the most common disappointment: a wine that turns out to taste completely different from what you expected.
If a term means nothing to you, ask specifically in the shop about its meaning in that particular region. A specific question usually gets a specific answer. If no one's around to ask, stick to the details you can confidently interpret. Leave the bottle's presentation out of the equation.