Applied dominants (i.e. secondary dominants) can be most easily identified as dominant chords that tonicize some harmonic triad or chord that is not acting as the tonic in the home key of the progression. We can also say this by saying that applied dominants are dominants that do not belong to the home key. To understand what these statements means, let me break them down into more digestible parts.
First: what is a dominant chord? Well, the theory of harmonic function is complex, and there are a number of different ways music theorists have approached it over time. The simplest and most practical way to define dominant chords are as any chord that is built on the 5th (V) or 7th (viidim) scale degrees in any given scale that has a leading tone (the seventh scale degree, or "ti" in solfege) that ascends by step to a tonic (or first scale degree).
If the dominant is built over the 5th scale degree, it will always consist of a major triad with an optional flatted (dominant) minor seventh over the root. The leading tone in this case will always be the third of the chord. If it is built over the 7th scale degree, it will always consist of a diminished triad, with an optional minor (half-diminished) or diminished seventh (fully diminished) over the root. In this case, the leading tone will always be the root! For example, in C major, the two chords that are usually labelled as "dominant" are G7 (G, B, D, F) and b half-diminished (B, D, F, A).
For extra credit: something we might note is that both of these dominants share an important interval: the tritone B, F in between the leading tone and fourth scale degrees! Virtually all dominants have this intervallic property: a tritone that resolves into the third of the tonic by semitone convergence (although in minor keys, the fourth scale degree will descend by whole step).
To identify when a dominant chord is "applied" we can ask ourselves the following questions: 1) does it behave like a dominant, and 2) does it resolve to the home key tonic?
In the chord progression being considered – F D7 Gm C7 Fmaj7 Bb/F F – there are four candidate dominants: F, D7, C7, and Bb/F. Each are either major triads, or "dominant chords" (with an added minor 7th over the root), so we can look at how they resolve and see if they behave like dominants.
1) F to D7: here the root lowers by minor third (instead of ascending by 4th or descending by 5th) and the third of the original triad (what would be the leading tone) is held over (A -> A) as a common tone. Furthermore, since 6 of the 7 chords in the progression belong to F major, we know that F is probably the tonic, so F does not behave like a dominant.
2) D7 to Gm: here we have a resolution by ascending 4th (D to G), and if we modeled the voice leading the third of the D& (F#) would ascend by semitone to the root of Gm (F# -> G) like a leading tone. Also, whenever we see a major chord with a minor seventh we can be virtually certain that it is a dominant (since they are rarely used in other ways), so D7 does behave like a dominant.
3) C7 to Fmaj7: is almost exactly the same as the previous, so for all the same reasons C7 does behave like a dominant.
4) Bb/F to F: this is close, but Bb resolves to F by ascending fifth, rather than by fourth, and having the tonic in the bass for both chords makes it pretty clear that this is a plagal cadence, so Bb/F does not behave like a dominant.
So this leaves us with two dominants – D7 and C7 – so now we can ask ourselves the next question: do they resolve to the home key's tonic. C7 resolves to Fmaj7, which is the tonic, meaning that C7 is just a regular dominant. D7, however, resolves to Gm which is not the tonic in F major. We would say, then, that D7 is tonicizing Gm; it is resolving to a non-tonic chord as if it were the tonic, treating it like a tonic and briefly pulling us away from the home key (only to have the remaining chords of the progression pull us right back).
This is the function of applied dominants: to trigger progressions that must resolve to non-tonic harmonies, adding a certain tension or color to chord progressions by introducing new chromatic elements. The D7 chord in this case introduces an F# to the F major key environment, a pitch that clashes interestingly with the tonic given its semi-tone proximity, and allows the composer or arranger to introduce interesting chromatic melodic flourishes to an otherwise banal progression. For example, the F# would allow us to link the F and Gm chords through a neat chromatic ascent somewhere in the harmonic texture: F – F# – G.
Our answer, then, is that in our progression only D7 is an applied dominant. Hopefully, however, the extended discussion above will help you identify basic applied dominants in any context, as well as appreciate what kinds of compositional possibilities they afford.
To summarize: to find applied dominants, look for 1) chords that behave like dominants (triads that belong to the dominant harmonic categories that resolve with a semitone connection to the root of the following chord) that 2) do not belong to the home key, do not point to or resolve to the tonic, and 3) also introduce chromatic motions involving pitch classes that aren't in the original key's diatonic (or minor) scale(s).
