Using Horner's Method I'm trying to evaluate a polynomial recursively using Horner's method.
It's rather simple when I have every value of $x$ (like: $x+x^2+x^3...$), but what if I'm missing some of those? Example: $-6+20x-10x^2+2x^4-7x^5+6x^7$.
I would also appreciate it if someone could explain the method in more detail, I've used the description listed here but would like some more explanation.

Horner's method or form is also sometimes called nested form.  You can think of it as starting with the whole polynomial $$6x^7-7x^5+2x^4-10x^2+20x-6,$$ setting aside the constant term (if it's zero, you can set aside a zero here) and factoring out an $x$ from the remaining terms $$(6x^6-7x^4+2x^3-10x+20)x-6,$$ and then repeating the process for the innermost polynomial (the part that isn't yet fully in nested form:
$$((6x^5-7x^3+2x^2-10)x+20)x-6$$
$$(((6x^4-7x^2+2x)x-10)x+20)x-6$$
$$((((6x^3-7x+2)x+0)x-10)x+20)x-6$$
$$(((((6x^2-7)x+2)x+0)x-10)x+20)x-6$$
$$((((((6x)x-7)x+2)x+0)x-10)x+20)x-6$$
$$(((((((6)x+0)x-7)x+2)x+0)x-10)x+20)x-6$$
Alternately, if your polynomial is $$p(x)=\sum_{k=0}^{n}a_kx^k=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,$$ you can think of $p(x)$ in nested form as $p_0$ where $p_n=a_n$ and $p_{k-1}=p_kx+a_{k-1}$.  That is, start with the leading coefficient ($a_n$).  Multiply by $x$ and add the next coefficient (adding zero to fill in for "missing" powers of $x$), repeating until you've added the constant term ($a_0$). Back to the same example:
$$\begin{align}
p_7&=6\\
p_6&=(6)x+0\\
p_5&=((6)x+0)x-7\\
p_4&=(((6)x+0)x-7)+2\\
p_3&=((((6)x+0)x-7)+2)x+0\\
p_2&=(((((6)x+0)x-7)+2)x+0)-10\\
p_1&=((((((6)x+0)x-7)+2)x+0)-10)+20\\
p_0&=(((((((6)x+0)x-7)+2)x+0)-10)+20)-6
\end{align}$$
