Let's say you are asked to calculate the pH of a solution with:

* $\mathrm{0.1~M}~\ce{HCl}$
* $\mathrm{0.2~M}~\ce{CH3COOH}$.
* $K\_\mathrm a = 2\times 10^{-5}$

This is how I would do it:

$$\ce{CH3COOH + H2O <=> H3O + CH3COO-}$$

The corresponding ICE table:
\begin{array}{|c|cccc|}\hline ~ & \ce{CH\_3COOH}& \ce{H\_2O}& \ce{H\_3O^+}& \ce{CH\_3COO^-}\\ \hline \mathrm I & 0.2 & & & 0.1\\\Delta & -x & & x & x\\ \mathrm E& 0.2-x & & x & 0.1 +x\\\hline\end{array}

calculate the pH:

$$\begin{align}
 K\_\mathrm a &= \frac{\ce{[H3O+][CH3COO^{-}]}}{[\ce{CH3COOH}]}\\
 &= \frac{x \cdot (0.1+ x)}{(0.2-x)}
\end{align}$$
as $x$ is very small, we leave it out:
$$\begin{align}
 \implies 2\times 10^{-5} &= \frac{0.1x}{0.2}\\
 \implies 2\times 10^{-5} &= \frac{0.1x}{0.2}\\
\implies~~~~~~~~~~~~ x &= 4\times 10^{-5}\\ \implies
 -\log(x) &= 4.40~= \mathrm{pH}\\
\end{align}$$

* First of all. Is this correct?
* Where do you include $\ce{HCl}$? I didn't write it anywhere. And I see most of the people not writing the second molecule. How/where is it included?
* What is the molecule in the first column of the ice table? What does it represent? Do you always write the acid in that column?

---

I made that exercise up. The original exercise has $0.1$ molar $\ce{HCl}$ and $0.1$ molar $\ce{CH3COOH}$. I changed it in order to clearly see which value is which one at which place in stead of all having the same ones. This is the original exercise: 

\begin{array}{|c|ccc|}\hline & \ce{CH\_3COOH} & \ce{H\_3O^+} & \ce{CH\_3COO^-}\\ \hline \mathrm I & 0.1 & & 0.1\\ \Delta& -x & x & x\\ \mathrm E &0.1-x & x & 0.1 +x\\ \hline\end{array}

\begin{align}K\_\mathrm a &= \frac{x\cdot (0.1 +x)}{(0.1-x)}\\ &\approx \frac{x\cdot 0.1}{0.1}\\ \implies x&= 2\times 10^{-5}\\\therefore -\log(x) &= 4.70\;. \end{align}