I see you're on a Mac.  There should be a keyboard app similar to Charmap on Windows (a native OS software like MS Paint).

In Windows there is a keyboard shortcut for this for fonts that have that glyph built in:  "Alt+0156" where the 0-1-5-6 is typed in sequence while holding the Alt button down.  The numbers must be typed from the numeric keypad on the right-hand side of the keyboard used for accounting applications.  Charmap from the command line typed out will bring up this application and will show you many keystroke equivalents but not every glyph has a keystroke equivalent.  I will look on the mac side to see what this application is called if you don't find it first.

Just a nominal footnote: "œ" is not a ligature, in the sense that "fi", "fl", and "Th" (in Minion Pro) are. These are typographic ligatures, designed to lighten the 'clash' between the top of the 'f' and 'i' -- and the other combinations. As such, they are used automatically when needed.

"Œ" on the other hand is a proper character on its own. There is a difference between "boeuf" and "bœuf", if only that the former has 5 characters and the latter only four. Ligatures do not change the character count, they only change appearance; digraphs such as 'œ' and 'æ' change the *meaning* of a character, and so it's beyond OpenType to "fix" it.

(Adobe used to add "œ" as a 'ligature' to fonts -- maybe as "Discretionary Ligature, cannot recall -- but ceased to when they got complaints from native users of these. A comparable, recent discussion on Typhophile was on 'automatic' replacement of 'ss' by 'ß' and the other way around. Again, this is not a pure typographic replacement but an orthographic one, beyond the scope and intention of OpenType.)

"œ" is not a ligature, in the sense that "fi", "fl", and "Th" (in Minion Pro) are.

The Oxford dictionary calls a ligature "two or more letters joined (fi, æ etc.)" from the Latin ligere to bind.

So presumnably œ is a ligature too.

Here in Iceland we use Æ, æ for the sound 'eye' and it remains a ligature of A and E even though it has its own place in the alphabet and is treated as a separate letter in its own right.

Personally, I use the term "ligature" exclusively for optional designed combinations of any two (or more -- "ffi") characters that do not influence "meaning", and "digraph" for a unique character that happens to be historically composed out of more characters.

That's your personal definition (which I understand to a point) but it's not the official one.

And by the way, "Ye olde" is really "Þe olde", the letter thorn having been mistaken for a Y in Gothic script. We still use Þ, þ in Icelandic for the unvoiced th sound like in thistle. See also http://www.baacorsham.co.uk/SFsubweb/PAGE7.HTM bottom of page.

Switchable ligatures like fi, fl, ffl, ct, st etc. might for that matter be called optional ligatures (cf. optional hyphens). That is to say you can do without them at the expense of pretty typography.