Apple - How to access Greek symbols on macOS from a basic keyboard without copy/paste?

In the top left-hand corner of the Character Viewer, there’s a gear icon. The first option is “Customise List…”.

This gives you a selectable list of all the character sets available in the sidebar. If you scroll down, you’ll find Greek as one of the options:

I don’t have a Mavericks machine to hand to check, but I’m fairly sure this feature existed before Yosemite.

Here's the neatest trick I've found for easily getting the Greek letters when I need them. In System Preferences -> Keyboard -> Shortcuts I have Select the previous input source mapped to cmd-space:

and then in Input Sources I have my standard keyboard and the Greek keyboard:

Now whenever I hit cmd-space my keyboard switches over to Γρεεκ (or vice-versa):

The Greek letters map to the English letters in a much more rational way than what you get with holding option and hunting/pecking. The one caveat is that cmd-space is natively mapped as a shortcut for something else, but considering that I can't even remember what that something else is it wasn't very important.

Edit:

For completeness, it turns out that cmd-space is normally a shortcut that brings up a Spotlight search bar.