Check the website you are visiting is secure
Before submitting your bank details or other sensitive information there are a couple of checks you can do to help ensure the site uses encryption to protect your personal data:
Check the web address in the address bar. If the website you are visiting is on a secure server it should start with "https://" ("s" for security) rather than the usual "http://".
Also look for a lock icon on the browser's status bar. You can check the level of encryption, expressed in bits, by hovering over the icon with your cursor.
Note that the fact that the website is using encryption doesn't necessarily mean that the website is legitimate. It only tells you that data is being sent in encrypted form.
Be cautious with emails and personal data
Most banks have a security page on their website with information on carrying out safe transactions, as well as the usual advice relating to personal data: never let anyone know your PINS or passwords, do not write them down, and do not use the same password for all your online accounts. Avoid opening or replying to spam emails as this will give the sender confirmation they have reached a live address. Use common sense when reading emails. If something seems implausible or too good to be true, then it probably is.