whim

I just spent some time hopping around on google trying to learn the proper usage of the term "whim" before giving in.
I thought I could say, " I had a whim to go skiing (NOT)," but I couldn't find a similar structure.

That sentence sounds off to me... I don't really use that word very much, though. I usually use it in the phrase "on a whim", e.g. "I went skiing on a whim." People also often say "every whim", as in "Why do you bow down to her every whim?"

That's what I found out from my "research."
But a phrase example on dictionary.com is what confused me:
"a sudden whim to take a night walk."
In an attempt to turn that into a complete sentence, I assumed that I could just add the verb 'had' in the beginning: 'I had a sudden whim to take a night walk." But I guess that that's off. The question remains: how can I make that phrase a sentence?

No, your sentence is fine.

The word "sudden" seems to make it okay. Without it, there's a sense that it is a continuous state, while with it, there's a sense that one had the whim for a moment, which makes more sense. A whim is not really something that one can have for an extended period of time. Otherwise it's not a whim anymore.

Since "whim" means "an odd or capricious notion or desire," saying "I had a whim" is essentially saying "I had an odd desire."

If the definition makes sense with the way you used the word, it's likely a correct usage.