Note Values- When and for how long to play notes?

So actually we all are playing by listening already created music. We listen to music and play accordingly but what if we created some sort of music and we need to write that piece of music on the sheet. Yes of course the tablature can do this but the tablature will not tell others how fast and for how long to play the given notes. If they know the song then they can play but if they don't know the original song then they never can play on actual speed.
In order to actually perform a piece of music, it is also essential to arrange the notes in the context of time; that is, it is necessary to know when and for how long to play them.

Beats and Meter: Ordinary clock time is divided into various units of measure, of which the smallest is one second. Musical time is also divided into units of measure, of which the smallest is the beat- the underlying regular rhythm of a piece of music. Just as seconds are grouped into minutes, repetitive patterns of strong and weak beats form the meter, or overall rhythmic feeling, of a piece of music. The meter usually consists of groups of 2, 3, or 4 beats, with the first beat of each group being the strongest, and this pattern usually stays the same throughout a piece of music in order to provide a consistent backdrop for the melody and harmony. The most common time signature is four beats in a measure.

What is pitch ?

Music is made up of sounds that can be organized into three main elements; melody, rhythm, and harmony. These elements are passed from one musician to another by music notation, which allows a reader to precisely locate and reproduce any musical sound by means of a set of symbols that represent both the pitch of a note (relative sense of high or low) and its rhythm (placement in time). We will look first at the symbols that represent pitch.
The system for representing the pitch is based on assigning a different name to each note. These note names are the same as the first seven letters of the alphabet "A, B, C, D, E, F, G, A" and together are called the musical alphabet. In spite of the large number of notes that can be produced by musical instruments, only seven note names are needed because the eighth note, called the octave, has the same sound as the first, but higher in pitch and therefore uses the same letter name as the first note. The octave is both the end of the first set  of notes and the beginning of the next. Different instruments are capable of producing sounds in different ranges of pitch, some in many different octaves and some in only a few, but all of these pitches are notated with the same seven letter names.

Confuse what is octave ? see the chart below of musical alphabets and octave:-

A    B    C    D    E    F    G    A    B    C    D    E    F    G 
1     2     3     4    5    6    7     8/1   2    3     4    5    6     7  
                                            octave