It's ok, you can admit it. You don't really get why decanting a wine, or "letting it breathe," is such a big deal. And you know what? That's totally fine! First of all, it's not a deal breaker for all but the nicest older wines that have a lot of sediment at the bottom. Other than that, no wine "needs" to be decanted. Plus, even if it benefits from some fresh air, you probably won't be drinking it fast enough to not have some level of opening up occur. (Ahem!...that is not a challenge!)
That said, many wines do improve, in some cases dramatically, with a minimal amount of time open to sweet, sweet oxygen. There are also some simple hacks you can use in most cases to speed up the process.
Before we get started on this topic, let's first answer a simple question: do you need a decanter? The short answer is probably not. Decanters are actually not designed to aerate wine. Aeration comes as an added bonus - or drawback, in some cases. Decanters instead serve to remove the sediment that builds up in wine as it ages in the bottle. Sediment can sometimes even be found in young wine that has a lot of extra stuff in it. This generally only applies to medium to big red wines, especially ones that are unfiltered, unfined, or older than 10 years. The sediment at the bottom of some red wines is in no way a sign of poor quality. In fact, it often signifies a fine wine. Said sediment is not, however, pleasant to consume. Hence the invention of the decanter!
So, the first thing we've determined is that if you know, or can reasonably assume, that a wine is going to have a sediment, then you should either use a decanter, or skip the last inch or so at the bottom of the bottle. Here are ways to determine that:
1) Is it red? Whites usually don't have enough extra particles floating in solution to form a significant sediment, so the only reason to use a decanter on a white would be to aerate it.
2) Do you know that the wine is unfiltered? There's a couple ways to determine this. The first is whether the producer tells you, generally as part of the marketing or label information. Many "natural wines," for instance, tout that they do not filter. The second is to know something about the region. More traditional regions often do not filter or fine (process by which tannins and other particles are removed or altered) their wines. The third is to see if whomever you're getting the wine from knows. Never be afraid to ask!
3) How old is it? The older the wine, the more likely that it has sediment.
4) What is the grape or blend of grapes? Are they thick-skinned, like Cabernet Sauvignon or Malbec, or thin-skinned, like Pinot Noir or Nebbiolo? While all of these grapes can leave sediment, Cab and Malbec will leave more sooner.
Ok, now that we've answered the question of whether you need a decanter, the next question is whether it's worth the expense. This depends on whether you drink the types of wines mentioned above, that would "throw a sediment." There's an aesthetic angle here as well: decanters are beautiful, so if you have the space, why not? You may not use it often, but when you do, at the very least it will be a conversation point. But for the purposes of aerating a wine, they are not necessary, as you will see below.
Now, on to the central question of when to aerate a wine, and how to do so!
Many more wines will benefit from breathing than need to have sediment removed. This is why the term "decant" and the term "aerate" have come to mean nearly the same thing to most wine drinkers. Decanters expose so much of a wine to oxygen that using one is generally the best way for a wine to open up. In addition, many of the characteristics that make a wine throw a sediment over time are the same characteristics that can key you into the need to let a wine breathe. The biggest and most important exception is very old age. Some old wines absolutely need to breathe. Others, you run the risk of blowing off the bouquet, the formation of which was a major point of aging the wine in the first place. Paradoxically, the very wines that decanters were made for are not always the ones that should be put in one. Sometimes you really just need to sacrifice the dregs of the bottle.
Here's a rundown of how to tell if a wine needs to breathe:
1) Open the bottle and pour about an 1/8th of a glass. Enough to smell and taste, but no more than that.
2) Give the wine a quick swirl, and give it a sniff. What do you smell? If the answer is nothing, you almost certainly need to aerate the wine. If the answer is a slight sulfur smell, it should also breathe for a bit. Finally, can you smell the wine, but certain tones are overly prevalent, or muted? If all you're smelling is the tones from oak, it needs to breathe. If you smell a bunch of things other than fruit, it most likely needs to breathe.
3) Take a sip. Are the tannins all you get? If your mouth tingles all over and the wine is slightly bitter, and you can't really taste much else, it needs to breathe. Does the wine taste too one-dimensional? Are you only getting one or two types of flavors, when you know the wine is supposed to be complex? Then it needs to...you get the idea.
4) Give the wine one final, intense swirl in the glass, and repeat. If the wine still feel "tight" or "off" or "limited," you know what to do.
There are multiple options for aerating a wine. The easiest thing to do is to pour yourself about half a glass, put the cork back in, put your thumb on it and give it a good shake for 5 seconds. The surface of the wine will be covered in bubbles, which means you did it right. This method has some caveats:
1) Don't do this to an elegant, light bodied red. In other words: never do this to a good Pinot Noir, or anything like one.
2) Even more important: Never do this to a wine that is more than 5 years old, no matter what type it is.
3) Though this will speed up the process, it's not the same thing as giving the wine time to breathe naturally.
The extension of this is to buy an aerator. While they're a bit gentler on the wine, and they do work, they're more a novelty item than a necessity.
Another method, which works for all wines, is to play a little psychological trick on yourself. There are a couple variations on this, but this is my favorite. Pour yourself a smaller than normal glass, but not much smaller, since it's your reward. Leave the cork off the bottle. Put the bottle far away from yourself, like the other side of the kitchen or even another room. Put the glass on the counter and tell yourself you're not going to touch it until you finish some task. If you're cooking, maybe it's when you get the dish into the oven. Whatever it is, try to make the task at least 10 minutes long. If after completing the task you've had enough and you need to cave, go grab the glass and get back to whatever you were doing. If you chug it, so be it, but you'll usually find that by this point you've involved yourself so much in the task at hand that you will drink this first glass pretty slowly. By the time you're ready for glass number two, most wines will have breathed well enough to give you the flavors you paid for.
Finally, be prepared for the inevitable wine that needs many hours to fully open up. Drinking a wine during this process is actually very fun, because each glass, really even each sip, will be different. You still want to give the wine an initial 30 - 60 mins though.
If you are hosting, just serve whites, roses, aperitifs, and light reds first, and leave the wines that need to breathe open. However, if you do so, you need pour a tiny bit out, otherwise the surface of the wine exposed to the air will not be big enough to make a difference. If you have multiple bottles of the same wine, pour a bit of each into one glass and put it aside for yourself for later. Or, if you know the wine that needs to breath is for the main course, go ahead and pour everyone's glasses ahead of time.
The final piece here is to always remember context. If you're at a house party and the wine you brought is a crowd pleasing sipper (or chugger), aeration shouldn't even be on your mind. If you're having anniversary dinner, take all the care you can to make sure the wine drinks perfectly. If you're hosting but most people won't really be paying too much attention to the wine, then all you really need to do is make sure you don't pour the end of the bottle (with all the sediment) into your mother-in-law's glass if you don't want to hear about it for the next 20 years.