I want to know how I can access the data stored in these variables...but I have no idea what N0$ for example stands for and how to extract the data from there into a register, for example.

    N0$:    .byte   DASH,DASH,DASH,DASH,DASH,END    ; 0
    N1$:    .byte   DOT,DASH,DASH,DASH,DASH,END     ; 1
    N2$:    .byte   DOT,DOT,DASH,DASH,DASH,END      ; 2
    N3$:    .byte   DOT,DOT,DOT,DASH,DASH,END       ; 3
    N4$:    .byte   DOT,DOT,DOT,DOT,DASH,END        ; 4
    N5$:    .byte   DOT,DOT,DOT,DOT,DOT,END         ; 5
    N6$:    .byte   DASH,DOT,DOT,DOT,DOT,END        ; 6
    N7$:    .byte   DASH,DASH,DOT,DOT,DOT,END       ; 7
    N8$:    .byte   DASH,DASH,DASH,DOT,DOT,END      ; 8
    N9$:    .byte   DASH,DASH,DASH,DASH,DOT,END     ; 9

    A$:     .byte   DOT,DASH,END                    ; A
    B$:     .byte   DASH,DOT,DOT,DOT,END            ; B
    C$:     .byte   DASH,DOT,DASH,DOT,END           ; C
    D$:     .byte   DASH,DOT,DOT,END                ; D
    E$:     .byte   DOT,END                         ; E
    F$:     .byte   DOT,DOT,DASH,DOT,END            ; F
    G$:     .byte   DASH,DASH,DOT,END               ; G
    H$:     .byte   DOT,DOT,DOT,DOT,END             ; H
    I$:     .byte   DOT,DOT,END                     ; I
    J$:     .byte   DOT,DASH,DASH,DASH,END          ; J
    K$:     .byte   DASH,DOT,DASH,END               ; K
    L$:     .byte   DOT,DASH,DOT,DOT,END            ; L
    M$:     .byte   DASH,DASH,END                   ; M
    N$:     .byte   DASH,DOT,END                    ; N
    O$      .byte   DASH,DASH,DASH,END              ; O
    P$:     .byte   DOT,DASH,DASH,DOT,END           ; P
    Q$:     .byte   DASH,DASH,DOT,DASH,END          ; Q
    R$:     .byte   DOT,DASH,DOT,END                ; R
    S$:     .byte   DOT,DOT,DOT,END                 ; S
    T$:     .byte   DASH,END                        ; T
    U$:     .byte   DOT,DOT,DASH,END                ; U
    V$:     .byte   DOT,DOT,DOT,DASH,END            ; V
    W$:     .byte   DOT,DASH,DASH,END               ; W
    X$:     .byte   DASH,DOT,DOT,DASH,END           ; X
    Y$:     .byte   DASH,DOT,DASH,DASH,END          ; Y
    Z$:     .byte   DASH,DASH,DOT,DOT,END           ; Z

but I have no idea what N0$ for example stands for

It clearly stands for the digit '0' in morse code. The dollar sign is just a character in the label name, nothing more. You access it like any other label/variable/identifier. Which assembler are you using?

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