This article refers to Opera versions 15 and onwards (the ones based on Chromium). If you want to make the older 12.x (Presto-based) version more secure, read the Securing Opera 12.x article instead.
Open Opera settings by clicking the big red O button in the top left corner and clicking Settings. Alternatively, use keyboard shortcut ALT+P for this.
Because Opera hides very important http and https parts of URL in address bar by default, open Browser tab, scroll to the end and tick the Show advanced settings box. Scroll up to the User interface section and enable the Show full URL in combined search and address bar option.
Here is the comparison of shortened (in top part) and full URL-s displayed in Opera's address bar. While a lock icon is displayed for secure connections, full addresses make it much easier to see if the current website is using secure (HTTPS) or non-secure (HTTP) connection.
Those who require extra security from drive-by-attacks and are fine with additional clicks to enable browser plug-ins (such as Java or Adobe Flash Player) should open Websites tab on the left and select Click to play from the Plug-ins section.
This feature prevents hidden malware on infected or malicious web pages from launching automatically. Click-to-play can be customized on per-site basis using the Manage exceptions button.
This means that all plug-ins on web pages are replaced with a clickable play button and "Click to run <plug-in name>" text as displayed in example below.
Scroll down the settings list and make sure that Do not allow any site to show pop-ups (recommended) is selected in the Pop-ups section.
Then select Do not allow any site to track my physical location in the Location section to disable sneaky geolocation features.
Notifications section should be set to Ask me when a site wants to show desktop notifications (recommended).
In the Media section, set the Do not allow sites to access my camera and microphone option.
Please note that you can still allow these features on certain sites by clicking the Manage exceptions button.
Click Privacy & security tab on the left.
Those very concerned about their privacy can clear the Use a prediction service to help complete searches and URLs typed in the address bar, Predict network actions to improve page load performance, Help improve Opera by sending feature usage information and Automatically send crash reports to Opera check boxes. These options send anonymous data about your behavior and browsing habits to Opera.
Always tick the Send a 'Do Not Track' request with your browsing traffic check box to prevent advertisers from storing and using your browsing habits.
Scroll down the list and clear the Offer to save passwords I enter on the web check box in Passwords section. Never use browsers for storing passwords - these are the first thing that any malware steals and decrypts! Install free Password Safe for storing and auto-filling credentials instead.
Finally, there's the Cookies section. Those extremely privacy-concerned, can activate the Keep local data only until I quit my browser and Block third-party cookies and site data options.
Most users should choose the Allow local data to be set (recommended) option.
Some sites may not work properly after you enable the Keep local data only until I quit my browser option, especially the ones with two-factor/two-step authentication. Common examples of 2FA include Google services (YouTube, GMail, etc), Microsoft accounts, Facebook, LinkedIn, Twitter, etc. To prevent login troubles on such sites, click the Manage exceptions button, input site names as instructed and choose Allow from the right. Click Done to apply changes - allowed cookies will be kept until they expire, or you choose to delete them manually
That's it - close the Settings browser tab to return to Opera.
Additional free security plugins for Opera
To stay away from malicious sites and downloads, use WOT Safe Surfing Tool. It also shows site ratings in search engine results (Google, Bing, etc) and on Facebook and Twitter.