Delete Opera's program files directory using Windows Explorer. It should be at "C:\Program Files\Opera" or "C:\Users\yourusername\AppData\Local\Programs\Opera".

If you don't want to keep your data and cache, also delete "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Stable" and "C:\Users\yourusername\AppData\Local\Opera Software\Opera Stable". You can delete the whole "Opera Software" folder for each if you don't have any other profiles in there you want to save.

Right-click on any Opera pinned taskbar icons and unpin. Unpin any Opera Start Menu icons. Also, delete any Opera shortcuts you have. See "C:\Users\yourusername\AppData\Roaming\Microsoft\Internet Explorer\Quick Launch", "C:\Users\yourusername\AppData\Roaming\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar" and "C:\ProgramData\Microsoft\Windows\Start Menu\Programs". Then, launch the task manager and restart the Windows Explorer process.

Delete all files and folders (or at least all of Opera's files and folders) in "C:\Windows\temp" and "C:\Users\yourusername\AppData\Local\temp".

Launch regedit and delete Opera's install keys. See Opera keys in "HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Uninstall" and "HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Uninstall".

Also in regedit, delete "HKEY_CURRENT_USER\Software\Opera Software", "HKEY_LOCAL_MACHINE\SOFTWARE\Clients\StartMenuInternet\OperaStable (look in "HKEY_CURRENT_USER\Software\Clients\StartMenuInternet" too for an Opera Stable key) and delete Opera strings from "HKEY_LOCAL_MACHINE\SOFTWARE\RegisteredApplications" and "HKEY_CURRENT_USER\Software\RegisteredApplications".

Also in regedit, delete "HKEY_CURRENT_USER\Software\Classes\OperaStable", "HKEY_LOCAL_MACHINE\SOFTWARE\Classes\OperaStable" and "HKEY_CLASSES_ROOT\OperaStable".

That'll get rid anything of importance. You can then search for "launcher.exe" and "opera" to find the rest and delete any things that you are sure are Opera-related. There are some Opera things in "HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\ApplicationAssociationToasts", but you don't have to delete them if you don't want to.

Then, you can reinstall Opera or another browser and set your default browser in Default Apps/Programs in Windows.