Two Simple Examples
First example is two bars of VAR. III from Mozart's Sonata A major K 331 (in fact bars 55 & 56):
We can see no signature, so it is either C major or A minor scale (other modes are not probable). First let's look at the full diatonic structure (as can be seen in Piano Trainer Practicing mode):
Here we can see more symptoms that it is really in A minor. We can see it mainly in bass line and in Harmony/Chords structure. Chords 6 and 3(+3) are diatonic minor tonic and dominant. Normally the 3 chord would be naturaly flat, here is sharpened what is not so obvious from notation, but there is a sign in the melody - the 6/5 tone. The proof is simple - try playing both variants of the chord and result is clear.
As concerns the convention generally, we will concentrate at melody line, bass line and harmonic structure (chords). We can notice that in this form each diatonic tone has it's own fixed color (covers melody and bass, chords are not considered as tones). For transitions in melody or bass line, we use convention of two neighboring numbers above each other (3/2, 6/5, 2/1).
Let's look at 'compressed' version of this. It is format we will usually use:
It contains all the same information, but rhytmic proportions are distorted in it (what is not seen here much), what is a price we pay for saving space. As well coloring is omited.
Now let's look at a bit more complicated example. Dvořák's Humoresque Op.101 No.7, end of A major section:
It is less straightforward than the Mozart's fragment. Let's look at the analysis chart. First the more explicit one:
Here we can see that we are again in diatonic minor mode. Except of 6 chord, we can see chord 4 and 26 (that was specially mentioned in the theory part) and dominant 3. The 3 here again in 'sharpened' version what not only makes it 'brighter' and it's 7-th extension makes it's dominant effect stronger, but BTW it is a dominat major with tendency to go to 6, that is root of the minor mode, that changes here to the root of major mode because here the scale changes to Gb (more in detailed analysis of this Dvořák's whole piece). In the bass line we can notice a 7 tone highlighted. The highlighting will happen always when a bass tone of a new chord is not the root of the chord, what is the case here.
Let's present the compressed version, that is the 'standard' format for further presentations:
Again we can see everything here too, with maybe a bit less comfort, but it is necessary if we want to present bigger areas of the compositions.