I was once told that you can determine an opening or transposed opening just by how the pawns are structured on the board. Is this the method normally used to determine if an opening was transposed into another through a sequence of moves? I have found it interesting how top players can usually see a transposition very quickly.
In one sense, I would simply say, "Yes, the pawn structure would be the first indicator that one has entered/transposed into a given opening." But since there's no other answer here as of yet, I'm going to take the liberty to say a bit more, pushing a little further than the question as you asked it.
Not to put too fine a point on it, but here's one way to look at this matter: it is not so much that the pawn structure allows you to recognize what opening you're in (or have transposed to), but rather that the pawn structure nearly defines a given opening. In fact, while at certain playing levels very precise knowledge of opening lines is definitely crucial, one can get quite far without focusing too much on particular openings, but instead just on particular structures, and understanding the sorts of plans and piece developments that are appropriate for given structures.
This kind of approach is very much in the proverbial spirit of being taught to fish, instead of being given a fish (read: an opening line). One can't be ignorant of particular lines entirely, as one could get "move-ordered" into positions/structures one does not want to play; my main point, though, is that I think many beginning and intermediate players overemphasize knowledge of particular opening lines, and can sometimes get too caught up on labels/names that, ultimately, don't really matter, and distract from more useful considerations.
Here's an example of what I mean. Consider a game that starts with a Trompowsky Attack move order,
1. d4 Nf6 2. Bg5, which then proceeds with
2. ... e6 3. e4 Be7 4. Nc3 d5 5. e5 Nfd7 6. Bxe7 Qxe7 7. f4, reaching the following position:
rnb1k2r/pppnqppp/4p3/3pP3/3P1P2/2N5/PPP3PP/R2QKBNR w KQkq - 0 1
This same position is reached much more often via a French Defense move order:
1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 Be7 5. e5 Nfd7 6. Bxe7 Qxe7 7. f4 (in my database, there are only 23 games which include the previous move order, but 4050 which include this one). So, though we started off with a Trompowsky, we've ended up in a position that would now be termed the Steinitz variation of the French Defense. But what's in a name, really? If the Trompowsky was as old as the French, maybe it would be the other way around and we would say that in the latter case what started as a French transposed to a Trompowsky.
Here's my point: how we got here doesn't matter once we're here, and what we call it doesn't matter either for our chess playing. I have actually heard players say, in analogous situations, something along the lines of, "Oh, so now I need to learn the French Defense too." But this doesn't really make sense, any more than it would for a French Defense player who goes for this position to think that she suddenly needs to start picking up books on the Trompowsky. What each player really needs is to understand the structure that arises, regardless of what move order is used to get there, and regardless of what name for an opening the position receives.
Having said all that, I should probably say something about "learning to fish." One good resource is Andrew Soltis' classic Pawn Structure Chess, which examines appropriate plans in given structures via many illustrative games, in chapters that are broken down by opening families, with titles like: The Caro-Slav Family, The Open Sicilian-English, The King's Indian Complex, The Panov Formation, etc. You'll find that the reader reviews in the link generally solidly endorse Soltis' book; so do folks like Jeremy Silman.
Another book which uses illustrative games to explain certain kinds of pawn structures is Dražen Marović's Understanding Pawn Play in Chess. One difference from Soltis' book is that the chapters are broken down by the concrete aspects of various pawn structures, with titles such as Isolated Pawns, Doubled Pawns, Pawn-Chains, Pawn-Islands, etc. John Donaldson gave a very positive review of Marović's book.
I'll also mention Hans Kmoch's older work Pawn Power in Chess from 1959, because I bought that book early on when I got into chess, and though I wasn't really prepared for it at the time, I think it has a lot going for it. You can get a good sense of the book and its worth from the preview and the reviews in the link. But as everyone who ever mentions this book will say in one way or another, Kmoch tries to be overly "scientific" in his approach and introduces a lot of unfortunate terminology that does more to obscure than enlighten. (For instance, leucopenia and melanpenia are coined for light-square and dark-square weaknesses, respectively.) But if you get past that kind of jargon, by just ignoring it best you can, there is truly useful information in the book, and it comes in the form of a typically inexpensive Dover edition.
In Andrew Soltis' book Pawn Structure Chess, he goes into great detail on the types of pawn positions you run into with specific openings, how they relate to other openings with similar structures, and when the transpositions are common.
I'd look into that resource and others like it for the specifics you're searching for.
Consider this example
[FEN ""] 1.e4 c5 2.Nf3 e6 3.d4 d5 4.e5 Nc6 5.c3
Here, we see a transition from the Sicilian system to the French system. Black decided to transpose by playing 3...d5 instead of 3...cxd4. White could accept the transposition in different ways. White got extra options compared to the normal French variation, where
[FEN ""] 1.e4 e6 2.d4 d5 3.Nf3
would be unwise since the e4 pawn is hanging. Therefore, white could probably get the better of the transposition shown in the first diagram, by choosing something different than 4.e5 (e.g. 4.exd5 followed by Bb5+ and O-O). All in all, the more opening systems you are familiar with, the better you become at transposing between them as well as recognizing transpositions. While an opening system is often defined by its pawn structures, since pawns cannot move backwards and therefore the pawn structure has a defining impact on the rest of the game. Every system has its own inherent pawn exchanges, e.g. c5xd4 in the Sicilian system, c4xb5 in the Volga gambit. Also, there are typical pawn formations (e.g. the d6, e6, f7, g6, h7 of the Sicilian Dragon). So there is actually no magic to it, other than memory and pattern recognition!