1 PASSWORD Don't make it personal; use a combination of impersonal letters and numbers. The longer, the better. Also change it regularly.
2 ANTI-VIRUS AND FIREWALL PROTECTION Highly recommended for online banking; these will keep the computer and its data safe and secure. Ensure you get the best protection available on the market.
3 SUSPICIOUS EMAIL/PHISHING Emails asking for credit card information and passwords. Legitimate online banks don't do that.
4 PROTECTING CREDIT AND DEBIT CARDS Typical website addresses begin with https:// on any pages where you enter sensitive information. Also ensure the transaction occurs in a secured environment.
5 ACCESS FROM PUBLIC NETWORK PLACES After completing the transactions, sign out of the online banking website. It's also advisable to clear cache memory and immediately close the browser once you're done.
Extracted from: http://savestanton.com/safety-tips-for-online-banking/