Fundamentals of Musical Theory:

The notation system in this and following summary is "Common Notation".
  Literally based as this introduction-like summary is, it is highly recommended by many experienced professors that learning with an instrument of any kind or some instrument-simulating app if available, for music is part raw sensation and part linguistic phenomenon.
  All pictures are from Coursera online courses.

Naming Musical Notes

mnemonics

A piece of sheet music is written on staves(五线谱), each of which contains five horizontal lines running across a page. Staves, the grid-like system, suggest that a note(音符), shown as a little hollow circle, may well be standing either in a gap between two adjacent lines or on one of the five lines.
　The right hand group consists of 5 notes, in an ascending order representing E, G, B, D, F(a mnemonic: Every Good Boy Deserves Fun); 4 notes in the left group, in the same order, are F, A, C, E(the word, FACE, as a remembering tip).
　The left most sign is the stave's clef(谱号), which we will discuss further in detail in later summaries. The clef shown above is a treble clef(高音谱号), or a G clef, placing E above Middle C(more on this soon).

Octaves

Why, you might wonder, there are more than one F and E in the stave shown above? That is because the two Fs and Es are in different pitches: the upper F or E is an octave(八度) higher than the lower ones. All the 7 notes have their respective an octave higher or lower versions:

"An octave higher or lower"

  Note that some of the notes outlies the stave, their relative positions are denoted by ledger lines. Also note that when the lower note is on the line, its octave above is on a space and visa-versa.
  This lower C with one ledger line is called 'Middle C’:

Middle C

  If we start from middle C, then end with C an octave higher in the alphabetic order(that is a C major scale), on a piano we will get:

a C major scale on a piano

  A black key always comes in the intervals between two white keys, intervals such as C and D, D and E, F and G etc, whereas there's no black key between E and F, B and C. The former kind of intervals is a tone(全音), for instance, the interval between C and D, while the latter kind a semitone(半音). In white notes, two sets of semitones have identified. The first set is between B and C:

a semitone

The other set is between E and F:

a semitone

  We can also re-write the scale pictured on the piano as follows, with T for a tone, S for a semitone:

a C major scale

  This scale is an example of a diatonic scale(全音音阶)——one that has a pattern of 2 semitones and 5 tones going from one octave to the next. More on scales will be covered on later summaries.