How do I perform a Discrete FFT by hand?

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I have understood the theory behind the Fourier Transform, but when I look at the formula on the internet there are multiple variables that are not explained. I know it is probably standard notation for this but I am self-taught and do not know what they are.

For example, how would I perform the FFT of [6, 7, 8]?

I am familiar with calculus and other topics, it is just this I'm struggling with.