Where to put the counterThis is perhaps the most natural question with embargo, and the one for which it has the multitude of possibilities. The general consensus on this issue has long been to put it where you have the most advantage over your opponents, i.e. if you have 2 more of a key card than your opponent, stick it there. However, figuring out where you have this advantage isn't always so simple, and in general, things can be more nuanced than that.
For instance, let's say the best thing on the board looks like it's a minion deck, and you have a 3-1 advantage on Minions when you play your embargo - your opponent has gotten some bad luck and has silvers instead. Traditional wisdom may have you slam that embargo down on your Minions, as that's where you have your lead. In general, this is going to be a mistake. 3 Minions doesn't make a Minion deck, and by locking each of you out from Minions, what you're basically doing there is making your minions much closer to her silvers, and that actually reduces your advantage.
Instead, you need to look at where you can cut their strategy off without cutting off your own. Or, failing that (as you often will), figure out if cutting both of you off is more beneficial to you or them. And failing both those things, finding somewhere to stick the token that it does nothing. Generally, there's going to be *somewhere* in which you have an advantage, and you will try to maximize that. In the case that you're just behind everywhere, you can try to minimize it by making the game some kind of bizarre luckfest - this probably won't work, but you were probably losing anyway.
EnginesEngines are often super reliant on a particular card - if it's the only village, if it's the only draw card, if it's the only +buy (though on the last point, once they've gotten a couple, that's often enough). Stopping this up can be pretty devastating for many opponents if you can do it soon enough. On the other hand, engines are often the kinds of decks which can most use the card - they're most likely to have the spare $2 and a buy laying around, and to be able to get back to the bought Embargo quickly
Big MoneyAt first glance, you might think that big money is not super dependent on any card, and thus pretty immune to Embargo, since there's usually some different options you can go with, and going down to the next one down usually wouldn't be just tons worse. However, there are some cards which Big Money is absolutely reliant on: the treasures! It's not super uncommon for a well-timed Embargo on Silver or Gold (or especially Fool's Gold) to be pretty devastating.
Other cursingThe most distinctive case where Embargo plays differently than all others is when there is some other curse-giver on board which is worth going for. The key thing to note here is that when you choose to embargo something, it's a far more temporary thing than normal: the curses will eventually run out, at which point it won't matter. So you want to pick something to delay both players getting to, rather than to really stop up. Of course, the big thing is if you can get a curser and then slam the door on your opponent. In this case, they should bite the bullet and get it anyway - otherwise, they'll lose 10-0.
TrashingTrashing is somewhat similar to cursing. Players will want to get their deck size under control, get to basically drawing it, before they start adding cursed cards. The difference here is that they will be slowed down in having to continually take some time - and often a terminal action - to trash a curse.
GainersGetting a gainer, then slamming down embargo tokens on the gainer pile, followed by another key pile, can be absolutely massive. This is especially true when the gainer IS the key card - such as with Horn of Plenty or most gainers with e.g. Highway present.
What about when to get Embargo?As it turns out, this is way more important to how the card plays than where to put it, although obviously the two things are related. In general, the big problem with Embargo is that it slows you down too much to buy it and play it. In other words, opportunity cost. The simplest explanation is, if you're wasting time buying a 2 cost, then drawing and playing that terminal action, your opponent is going to be getting good cards for their deck. You need to have your 1-shot $2 of economy be worth MORE than what they have done in the mean-time, and even if you shut down some strategy, chances are they can just audible into yours, and because you wasted time doing the Embargo thing, there's a very good chance they'll be ahead of you, even if their buys weren't optimal for what you were planning. I would be remiss if I didn't note that part of the problem is that usually when you buy the card, you can't count on having any particular advantage by the time you draw it, or if you wait until you're drawing your deck, the curses are less likely to be so impactful.
There are lots of exceptions, of course. The #1 case is, of course, on one of the first two turns of the game, when there aren't any other decent 2s - i.e. the opportunity cost is getting nothing. Beyond this, there are a number of times where you might have the terminal space (and card space) and a spare $2 and a buy, but it doesn't come up much - and pretty often, there are other, better 2s anyway. But when it does come up, it will most often be in an engine.
There are also a number of roads the opponent can go down which commit them to needing lot so fa particular card to have any success. Foremost here are potion-cost cards. You can make a move to bet your embargo as soon as they get their potion, and that means they're going, on average, to probably get just under one of their intended target before you can get the token down (obviously it depends a bit on the shuffles). Depending on which card this is, this can be very profitable. It seems like you could make a similar play on Treasure Map, but the problem there is, if Map is good, it's probably either for Trash for Benefit and/or they'll be able to trigger pretty reliably with exceptional sifting - which means that your embargo will probably be either too late or ineffectual. The same kind of thing is true for Fool's Gold - they will get 3-4 by the time you get your token down, and that is usually going to be enough that you won't be much up. It's actually pretty disastrous for you if you're missing a shuffle or they have extra gains - if they can get to something like 5 Fool's Golds, the game is probably reasonably close to being over...
Examples (certainly not comprehensive, as the most common thing is that you should just not buy the card)http://www.gokosalvager.com/static/logprettifier.html?/20151001/log.514b5511e4b0b79c883b5e3b.1443719767909.txt
Probably my favorite trick with Embargo is to stick the token on curses and use that as a way to pile out fast. This is actually a tactical little trick to keep an eye out for, though obviously it requires a big lead. In this game, my opponent does half the work for me :)
In this game, my opponent gets a token down on Gardens. I shrug this off pretty easily, as my deck doesn't really want to hit tons of money anyway, playing a slog. The second token, though, is on Copper! And this is surprisingly more effectual, as quite a bit of my plan was to buy a zillion coppers per turn, and carrying a curse is too steep a price for that. I do have to look at some point, once again, for piling out curses, but the bigger saving grace for me is that A) coppers weren't tainted earlier, and B) gaining silver is also very good for the slog.