Squared symbol (superscript 2)?

Launch the character viewer (aka Edit menu : Emoji & Symbols) or ⌃⌘-spacebar. Enter superscript as shown in the image, and double-click on the particular number (e.g. 2) that you want entered in the current application location.

You could also visit the System Preferences : Keyboard panel, and the Text tab. There, you can enter an abbreviation for a superscript 2 (e.g. ^2) in the replace column, and after tabbing over to its With column, you perform the first sentence of the first paragraph, followed by a return to set the With item. Then in the Edit menu : Substitutions, you would select Text Replacement. Typing ^2 would show you a superscript 2 for replacement at that insert location.

Some word processing applications have superscript somewhere on their format menu, and you would select an ordinary 2 before applying the superscript.

Unfortunately this document is only the Sierra version and offers some features not in Mavericks, but a limited Mavericks version is available:

macOS Sierra: Replace text and punctuation in documents

https://support.apple.com/kb/PH25699

This trick will also only work in applications which offer Automatic Text Replacement which might well overlap to a large extent with applications which offer superscript already, making it of limited usage. You'll either see it as an item you can activate in the Edit menu or you won't. I also found it as "Text Replacement" under Edit > Substitutions in TextEdit.

Here's how I set it up in my Mavericks System Preferences > Keyboard

this results in:

in Mavericks TextEdit. Just continue typing and it will enter the correction, so x squared is x^^2 (or whatever your preferred code to tell it to do the correction.

The only thing is, I think I noticed my computer slow own a little bit after adding these. Given that 99% of the writing I do these days is in my Waterfox(Firefox) web browser and the substitutions don't work there (and certainly not in the Apple Support Communities editor), I may deactivate them again.

I couldn't find one (and I use Mavericks) and this article outlines the options I could think of:

https://apple.stackexchange.com/questions/43845/how-do-i-type-a-%C2%B2-or-a-%C2%B3-on-an-apple-keyboard-international-english-layout

I think the preferred option will depend upon how frequently you need it and the software you are using (some editors have easy access to superscript, other not). For the frequency I need it I'd probably just find a web page with it and see if I could copy and paste it. ²

You can even take that character and make it part of a file or folder name. Store some of these harder to get characters as part of folder or file names and keep in a special folder somewhere for easy access. Copy it from the folder name and paste it where you need it.

Firefox does not implement the same Edit menu as does Safari. The latter does support Text Replacment in the community's editor. I can type -> in the editor with Text Replacement off and ➝ with Text Replacement enabled.

Good to know but I think the OP is asking about this for Mavericks. Apple hasn't updated Mavericks Safari in years and the new ASC doesn't work with Safari 9.1.3.