Youtube is owned by Google and you need a Google account to sign in. Click 'Sign In' at the top right of any Youtube page. Then click on 'More Options', followed by 'Create Account'.
Having a Google (or gmail) account is a good thing nowadays if you have an Android phone, or wish to use YouTube and so on.
Also it makes a perfectly good email account, and far better than using one linked to your ISP (if you ever decide to move from your ISP it can cause problems).
Do make a note of your new "gmail" email address (and password of course) as you will need it to log on later.