It entirely depends on the bank you're using. Usually though, most of them have an online portal you can register using the details that your bank gave you.
Most of the times you need to provide your credit card number as well as some details like account number or passcode that will be given with an instrument that automatically generates new passcodes.
Once you log in, the process will be pretty straightforward: Online banking procedures are always fairly easy so I am pretty sure there will be an home page which will display your saving account information and other things you might wish to check out. You can also transfer money or invest them online.
Note that some old bank account do not have an online access activated, but you can call your bank and sign up for it. You will only need to ask them to activate an account and they will give you all the details and information you need.
Hope this helps!