Use the rotate instructions, making sure the carry flag is clear before that.
For the 8051 assume the byte to rotate is in the accumulator, for the PIc assume it's in file register named Byte.
Ex 8051
clr C
rlc A ;for shift left
rrc A ;for shift right
Ex PIC18
bcf STATUS,C
rlcf Byte ;for left shift
rrcf Byte; for right shift
If you need multiple shifts, repeat the above steps the required # of times.