What exactly is the CW complex structure on a geometric realisation? This is likely a silly question.
Definitions:
$\bullet$ $\Delta_n = \{ (t_0, \dots, t_n) \: | \: 0 \leq t_i \leq 1, \sum_i t_i = 1 \}$
$\bullet$ Given $f: \underline{m} \to \underline{n}$ in $\Delta$, we have a map $\tilde f: \Delta_m \to \Delta_n$ given by $(s_0, \dots, s_m) \mapsto (t_0, \dots, t_n)$, where $t_i = \sum_{f(j) = i} s_j$. 
$\bullet$ Given a simplicial set $F: \Delta^{\text{op}} \to \underline{\text{Sets}}$, we have its geometric realisation

$|F| := \coprod_{n \geq 0} F(n) \times \Delta_n/ \sim$ 

where $(x, \tilde f (s)) \in F(n) \times \Delta_n$ is equivalent to $(F(f)(x), s) \in F(m) \times \Delta_m$ for $f: \underline{m} \to \underline{n}$.
$|F|$ is a CW complex with a $n$-cell for each nondegenerate $n$-simplex. 

May you please explicitly describe how $|F|$ is given the structure of a CW complex?


To see why the geometric realization of a simplicial set is a CW complex, let us describe the geometric realization inductively. The zero skeleton of $|F|$ will be $\coprod_{\Delta^0\to F}|\Delta^0|$, which is just a bunch of points. Now suppose that we have described the $n-1$ skeleton, $sk_{n-1}|F|$ at this point, we attaching a copy of $|\Delta^n|$ for each non-degenerate n-simplex, $\sigma:\Delta^n\to F$ along the map $|\partial\sigma|:|\partial\Delta^n|\to |F|$  (we know that this maps is defined by the induction hypothesis). In categorical language, we are forming the pushout of the following diagram to obtain the n-skeleton.
$$sk_{n-1}|F|\leftarrow \coprod_{\sigma\in N_nF}|\partial\Delta^n|\rightarrow \coprod_{\sigma\in D_nF}|\Delta^n|$$ where $N_nF$ is the set of non-degenerate n-simplices. For a reference to this see page 8 of Goerss and Jardine.
