This task has three parts:

 Connect to a MySQL database (connect_db)
 Create user/password records in the following table (create_user)
 Authenticate login requests against the table (authenticate_user)
This is the table definition:

CREATE TABLE users (
    userid INT PRIMARY KEY AUTO_INCREMENT,
    username VARCHAR(32) UNIQUE KEY NOT NULL,
    pass_salt tinyblob NOT NULL,
            -- a string of 16 random bytes
    pass_md5 tinyblob NOT NULL
            -- binary MD5 hash of pass_salt concatenated with the password
);
(pass_salt and pass_md5 would be binary(16) values, but MySQL versions before 5.0.15 strip trailing spaces when selecting them.)

import mysql.connector 
import hashlib
 
import sys	 
import random	 
 
DB_HOST = "localhost"	 
DB_USER = "devel" 
DB_PASS = "devel"	 
DB_NAME = "test"	 
 
def connect_db():	 
    ''' Try to connect DB and return DB instance, if not, return False '''	 
    try:	 
        return mysql.connector.connect(host=DB_HOST, user=DB_USER, passwd=DB_PASS, db=DB_NAME)	 
    except:	 
        return False	 
 
def create_user(username, passwd):	 
    ''' if user was successfully created, returns its ID; returns None on error '''	 
    db = connect_db()	 
    if not db:	 
        print "Can't connect MySQL!"
        return None
 
    cursor = db.cursor()	 
 
    salt = randomValue(16)	 	 
    passwd_md5 = hashlib.md5(salt+passwd).hexdigest()	 
 
    # If username already taken, inform it	 
    try:	 
        cursor.execute("INSERT INTO users (`username`, `pass_salt`, `pass_md5`) VALUES (%s, %s, %s)", (username, salt, passwd_md5)) 
        cursor.execute("SELECT userid FROM users WHERE username=%s", (username,) ) 
        id = cursor.fetchone()
        db.commit()
        cursor.close()
        db.close()
        return id[0]	 
    except:	 
        print 'Username was already taken. Please select another'	 
        return None
 
def authenticate_user(username, passwd):	 
    db = connect_db()	 
    if not db:	 
        print "Can't connect MySQL!"
        return False
 
    cursor = db.cursor()	 
 
    cursor.execute("SELECT pass_salt, pass_md5 FROM users WHERE username=%s", (username,))
 
    row = cursor.fetchone()
    cursor.close()
    db.close()
    if row is None:     # username not found
        return False
    salt = row[0]
    correct_md5 = row[1]
    tried_md5 = hashlib.md5(salt+passwd).hexdigest()
    return correct_md5 == tried_md5
 
def randomValue(length):	 
    ''' Creates random value with given length'''	 
    salt_chars = 'abcdefghijklmnopqrstuvwxyz0123456789'
 
    return ''.join(random.choice(salt_chars) for x in range(length))
 
if __name__ == '__main__':	 
    user = randomValue(10)
    passwd = randomValue(16)	 
 
    new_user_id = create_user(user, passwd)
    if new_user_id is None:
        print 'Failed to create user %s' % user
        sys.exit(1)
    auth = authenticate_user(user, passwd)	 
    if auth:	 
        print 'User %s authenticated successfully' % user	 
    else:	 
        print 'User %s failed' % user
 