Log out from ALL Google services. (NOT just from Youtube). i.e. go here and log out via the button at the top right (if you need to, of course):
https://www.google.co.uk
Go to
https://www.youtube.com/ and check that you're not logged in (again, at the top right).
Click 'Sign In'
Enter your email address and (on the next screen) your password.
If you've not changed the default settings you should then be offered a list of all the Youtube channels associated with your account (under 'Use Youtube as'), enabling you to choose the one you want.
However, if you've previously ticked 'Don't ask me again' at the bottom of that window, you'll automatically be logged into whichever channel you wanted to use at that time. If that happens, click the button at the top right of your screen and select 'Change account'. You'll then be offered the full list of channels.