CLC makes CF = 0, STC makes CF = 1, and CMC flips it. No other flag and no register changes. They are one byte each.

Uses

Returning success or failure from a procedure: DOS and the BIOS set CF = 1 on error, and your own procedures can do the same, ending with CLC / RET on success or STC / RET on failure, so the caller writes a single JC. The flag survives RET and POP, which do not change flags.

Preparing a chain: before the first ADC or RCL of a loop, CLC gives a clean start, so the same loop body can handle every word of a long number. STC feeds a 1 into RCL / RCR.

CMC turns a comparison around without a jump. After CMP AL, 10, CF = 1 means AL is below 10 (unsigned); a CMC makes CF = 1 mean "10 or more". The procedure below reports "not a digit" in CF that way.

Change 12 to 7 and it prints 7 instead of ?.
MOV     AL, 12
CALL    CHKDIG
JC      BAD1     ; 12 is not a digit
ADD     AL, '0'  ; digit -> character
MOV     DL, AL
MOV     AH, 02h  ; DOS: print DL
INT     21h
JMP     DONE1
BAD1:
MOV     DL, '?'
MOV     AH, 02h
INT     21h
DONE1:
 
; CHKDIG: CF = 1 when AL is not 0..9
CHKDIG  PROC    NEAR
CMP     AL, 10   ; CF = 1 when AL < 10
CMC              ; flip: CF = 1 when AL >= 10
RET
CHKDIG  ENDP

Do not confuse them with INC / DEC, which leave CF alone: that is why a multi-word loop can use INC SI between ADCs. Only CF has all three instructions; DF has CLD / STD, IF has CLI / STI, and the others are set with PUSHF / POPF or SAHF.