Hi Blackwatch.
You can't actually "Delete" Cortana (I've tried that several times and it reappears within seconds) but you can disable it. Microsoft have been very cunning with Windows 10 though. If you look in the settings box [Settings > System and then check the whole list], they share your info with all sorts of Apps. It's best to go through those lists and remove the "ticks" from some of the boxes as well as disabling Cortana.
To disable Cortana click (LMB) on the start icon (the white square with the black cross.) You should then see a load of blue squares - calender, mail, films & TV etc. One of those should be Cortana. Click on it and then click on the settings icon (should be second one down.) Turn Cortana off. When you've done that click on "Manage what Cortana knows about me in the cloud." This is where Microsoft have sent everything they know about you from your computer.
It will ask you to sign in with your Microsoft account username and password and then deliver you to
http://www.bing.com/account/personalization. Scroll down to the bottom of the page and find the "Clear" icon. Click on it and the job is done.
Be aware too that when you install Windows 10, if you came straight from Windows 7 it gets you to create a Microsoft account (usually using your e-mail username as the username for the Microsoft account.) Most people think this is the only way to "Log on" to their computer each time because Microsoft lets you believe that. However, you can log on WITHOUT using a Microsoft account and you will get no intrusions from nosey Bing etc. (I've deleted Bing from everywhere I've found it. It's crap and it's one of Microsoft's spies anyway.) Just go to Settings > Accounts > Sign in options and, if you haven't done so before, create a "Local" account and use that to log on. Simples!
If you get stuck have a look here:
http://www.digitaltrends.com/computing/ ... indows-10/
http://www.howtogeek.com/224546/how-to- ... indows-10/
Dave