INT 21h AH=19h returns the current drive in AL, counted from 0: A = 0, B = 1, C = 2. It cannot fail and changes nothing else. Adding the character "A" (41h) turns the number into its letter:

prints: the current drive is C:
MOV     DX, OFFSET MSG1
MOV     AH, 09h
INT     21h
MOV     AH, 19h  ; DOS: the current drive in AL
INT     21h
ADD     AL, "A"  ; 0 = A, 1 = B, 2 = C...
MOV     DL, AL
MOV     AH, 02h  ; DOS: print DL
INT     21h
MOV     DL, ":"
MOV     AH, 02h
INT     21h
MOV     DX, OFFSET CRLF
MOV     AH, 09h
INT     21h
 
MSG1    DB      "the current drive is $"
CRLF    DB      13, 10, "$"

Programs call it to build full path names (the letter, then ":\" and the directory from INT 21h AH=47h), and to save the drive before switching with INT 21h AH=0Eh, so they can switch back.

Counting from 0, and from 1

DOS numbers drives two ways, and mixing them up gives an off-by-one that points at the wrong drive:

ServiceDrive numbers
0Eh select, 19h get0 = A, 1 = B, 2 = C
36h free space, 47h current directory, 1Ch allocation information0 = the current drive, 1 = A, 2 = B, 3 = C
FCBs, byte 00 = the current drive, 1 = A
BIOS INT 13hnot letters but units: 0 = first floppy, 80h = first hard disk

So the drive 19h returns has to be incremented before it is passed to 36h or 47h, which is why both of those accept 0 for the current drive: it saves the call.