Notice the difference between the following blocks of code.
(If these don't work, then your issue is that pyserial did not install properly, and you should tell us how you tried to install it).
This just imports the function Serial from the serial module into your namespace
from serial import Serial
sr = Serial('COM4', 9600) # Serial is imported into your namespace,
# not serial, the module
This just imports the module serial into your namespace
import serial
sr = serial.Serial('COM4', 9600) # serial module is in your namespace
This imports all functions from the serial module into your namespace
from serial import *
sr = Serial('COM4', 9600) # the Serial function is imported into your namespace,
# not serial, the module
This imports the serial module, and gives it an alias name
import serial as s
sr = s.Serial('COM4', 9600)
The differences are subtle, but significant. Hope this helps.