How do I get better at tasting?

You get better through concentration and lack of distractions. Just as you shouldn't eat while watching TV. You'll miss all the flavors.

Sit back. Take small samples. Let it lay or slosh around in your mouth for a while--several seconds at least. Think about what you taste and feel.

Soon you will find those one-tone flavors have a background to them or a subtle second or third flavor coming out of nowhere.

After a while, you'll start noticing those underlying flavors every time you use that ingredient and notice it missing when you have a not-so-good variety.

You can improve by tasting things up and taking notes.

In the case of wines, which I'm more familiar, (and other alcohol) you can usually find local wine tasting groups, or when it is OK, go to a wine bar and get small pours of different wines and taste and take notes; ask before if you can do that, and do it at off-peak time. (and don't drink and drive)

For other products, try to find specialty stores for the product you want to taste, sometimes they can sell small sample of different products they have.

For example, my local chocolate store can sell me a sample box of different chocolate, white, milk and dark chocolate of different level of cocoa (50%, 70%...)

good luck.

Another approach you could take is by starting to bake/cook. If you understand how to create something, e.g. a cake or a curry, you can start experimenting with changing the amounts of flavours and seeing how that impacts the end result.

Adding lemon zest to a cake creates a really different result than leaving it out. Adding more or less cumin to a curry changes the flavor at the end. Eventually you get comfortable with guessing the impact of those little tweaks, and I find that this also makes me better at determining what I'm eating in a restaurant.

There's also the fun challenge of trying to recreate what you tasted earlier, for which you have to pay careful attention while eating and maybe even take some notes.

Source: I've been baking with my mother from a very young age. Due to a pesky food intolerance there were hardly any baked goods we could get from the stores. My mother took it up like a champ, became a baking machine and shared those baking sessions with me.

There are different factors, that influence taste:

Personal human limits: Everything that contributes to taste has a threshold, at which it becomes perceptible. Humans have different thresholds to different chemical compounds, so it may taste different to you, than to someone else.

Treating your palate right: Being able to taste subtle flavours is sometimes a matter of contrast. Regular consumption of sodas, strong coffee, super sweet stuff, etc. will make it harder to pick up subtle notes. If you really want to improve your perceptiveness you should avoid food and drinks that impart the "extremes".

Having a framework and learning: For me the major thing about "learning how to taste" is the vocabulary. It helps to describe what you taste and learning which differences two similar flavour descriptors have, helped me to learn the nuances. For example in beers most flavours are really subtle. It might be easy to find out, that a certain beer tastes like tropical fruits, but then differentiating peach, mango, lime, orange, etc. is a lot harder. It helps to have common examples of that descriptors or even the "pure thing" at hand to learn flavour descriptors.
I would say, that I've been able to taste all these things before, but I didn't had the right framework to differentiate the flavours that much.

Speaking of drinks again, for me it helps to focus on a certain aspect when having a sip: For example I focus on what flavour strikes me at first when taking a sip, then with the next sip I concentrate on how it develops, and then what the aftertaste is.

Sense of smell can play a big role in how you taste food. It is important to really smell your food before you eat it. Also make sure to breathe properly while you are eating. One trick that has always fascinated me is I can be munching on some walnuts and when I walk outside they actually taste different.

Other than that, if you practice it, your perception of tastes will become better too. Wines are great to practice with because winemakers are heavily invested in consistency and standing out subtly, but honestly I think it would work with any food, especially if you can practice on something familiar.

One thing to keep in mind is you probably won't taste the same things/way as other people. Unless your goal here is to eventually get into professional tasting, then don't worry about trying to taste 'a hint of citrus with overtones of elderberry' or whatever in your wines. Instead, focus on the tastes that are coming to you in whatever language or description seems to fit the best. And have fun!