How do I remove words from my personal dictionary?

Stored in /Users/"username"/Library/Spelling/LocalDictionary

Open it in TextEdit and delete the erroneous entry. Getting to the stupidly hidden Library folder is left as an exercise. I've permanently unhid it using this Terminal command:

chflags nohidden ~/Library

Might take a restart to take affect.

You can get to the User's Library by holding down the Option key and selecting the Go menu, when in the Finder.

So, how about words stored in the Global Dictionary? Will they be stored in the same place? (I'm more sure it I have ever added a word to the Global Dictionary.)

As of macOS 10.12.1, holding the Option key no longer shows the Library menu. Instead, you can use the Finder Go menu to Go To Folder: "~/Library/Spelling" (excluding the quotes), then open and edit the file named LocalDictionary.