ADD and INC

Add AL,1 will add 1 to the AL register and store the result in the AL register.
I think you can figure out what INC AL does on your own.

If a calculation gives a zero answer, set the Z zero flag.
If a calculation gives a negative answer, set the S sign flag.
If a calculation overflows, set the O overflow flag.

An overflow happens if the result of a calculation has more bits than will fit into the available register. With 8 bit registers, the largest numbers that fit are -128 to + 127.