Keep a close eye on bank statements, and dispute any unauthorized charges or withdrawals immediately.
While making a payment over the internet, check for the security logo on the website confirming it as a safe site. If in doubt, check with the concerned company before making any such payment.
Never attempt to access Online Banking internet through an external link of unknown or suspicious origin appearing on other websites, search engines or e-mails.
Avoid using Online Banking from public shared PCs (as in internet cafes, libraries, etc.) to avoid the risk of having your sensitive private information copied and abused.