Using WebDriver, you're free to use all the features of your programming language of choice. And that gives a lot of opportunities to structure your tests in such a way as to avoid code repetition.
If you're new to Selenium, I'd skip Page Object Model until you get comfortable with WebDriver basics. Until then, I would just wrap the frequently used code into functions and put those functions into a separate library/module that you can use in your test cases.
Let's assume you're using Python and you repeat the code for logging in all the time. For the sake of simplicity, let's also assume that navigation to the login page is taken care of separately in the test cases, and that the login form elements have stable, unique IDs. In such a case, you can write a function like this:
def login(user, password):
user_field = driver.find_element_by_id("user")
password_field = driver.find_element_by_name("password")
login_button = driver.find_element_by_name("log-on")
Then, whenever you need to login from a test case, you just call your function:
This is greatly simplified, but should give you an idea.