For reading deeper, we can use certain pieces of knowledge and use them alone, and/or in tandem. Here's a list of ways to read better, faster, smarter. When you know all of these things & can put them to work, you know how to read at a deeper level.
A key signature indicates which group of tones we will be using for a piece of music. It is indicated by sharps or flats which appear between the treble clef and the time signature in music notation.
To learn our key signatures for reading, we use visual resources, memorization, and playing scales.
Knowing our tone set (the key) helps us with the next thing on this list...same, stepping and skipping. For steps, we know whether we are moving up or down a minor or Major 2nd because we know the scale, and, for skips, which type of intervals we are moving to, whether up or down (how far?).
From a note, staying on the same line or space is the same. Playing the next available line or space, up or down, is a step. Playing a note bigger than a step is called a skip.
When we play a scale, one tone to the next to the next, this is playing in steps (2nds). Steps are 2nds. E to F is a 2nd. F to G is a 2nd. Yet, E to F is one fret, while F to G is two frets. Therefore, there must be two types of 2nds [a one fret 2nd, & two fret 2nd]. This is true. And, this idea applies to 2nds, 3rds, 6ths, & 7ths.
A one fret 2nd is called a minor 2nd [m2] = 1 half-step = 1 fret
A two fret 2nd is called a Major 2nd [M2] = 2 half-steps = 2 frets
For skips, the question will be, "how far?".
Visually, it helps to know what follows. In music notation rules, visual spacing allows use to quickly identify interval types. Pairing this information with knowledge of the fretboard and guitar intervals, we can interpret more efficiently, even without having to keep note-tone names in mind, as in the case of transposition (playing something in a different/new key).
Whatever line or space the note is on, is the line or space you start counting from (it is the 1). In the example, the first line of the staff, E, is 1, since the note-head is on that line.
When E is 1, the F space is some type of 2, the G line is some type of 3, the A space is some type of 4, the B line is some type of 5, the C space is some type of 6, the D line is some type of 7, the E space is some type of 8.
The type will depend on whether the tones are naturals, sharps, or flats [aka the key signature].
With time & practice, we can quickly identify interval types in notation by how they look (and how they translate onto the board - see Intervals on the Guitar). The challenge can be what type of 2, 3, 6, etc. This will depend on the key signature and whether sharps or flats are present.
And our final piece of knowledge to add to our deep reading list is how notation interval shapes translate onto the fretboard.
The black dot is any root [the lower down the string the root is located, the nut cuts off some of the possibilities – this is true for any string].
Check out the rest of the fretboard maps on the intervals on the guitar resource (in Theory/Mapping in the Nucleus).
Unifying all of the knowledge leads to this: when we see shapes and visual relationships in music notation, those entities mean something to our hands. We can build intervallic shapes quickly (our hands respond - snap into formations - through visual information).
The deeper our understanding, the more powerful are our realizations.