You can use this method to multiply long numbers together. The key insight you need is that polynomial multiplication is the same as normal long number multiplication without doing carrying.

So suppose you have a 1000 digit number. You then take each digit and use it as the coefficient of a 1000 element polynomial. You can then multiply these polynomials together using the fft method as described in the article. To convert the result back to a number you need to do the carries. So if an element is bigger than 10 you carry the excess to the next digit. You then take the coefficients and turn them into numbers.

That's the basic idea. There is some subtlety I've glossed over due to precision needed for the carries and to be sure that rounding the fft result to the nearest integer is correct. That is the way big number multiplication is done in GMP which is the leading Library for this sort of thing.