  Let $\mathbb F$ denote an algebraically closed field, and fix a nonzero $q
\in \mathbb F$ that is not a root of unity. We consider the $q$-tetrahedron
algebra $\boxtimes_q$ over $\mathbb F$. It is known that each
finite-dimensional irreducible $\boxtimes_q$-module of type 1 is a tensor
product of evaluation modules. This paper contains a comprehensive description
of the evaluation modules for $\boxtimes_q$. This description includes the
following topics. Given an evaluation module $V$ for $\boxtimes_q$, we display
24 bases for $V$ that we find attractive. For each basis we give the matrices
that represent the $\boxtimes_q$-generators. We give the transition matrices
between certain pairs of bases among the 24. It is known that the cyclic group
$\Z_4$ acts on $\boxtimes_q$ as a group of automorphisms. We describe what
happens when $V$ is twisted via an element of $\Z_4$. We discuss how evaluation
modules for $\boxtimes_q$ are related to Leonard pairs of $q$-Racah type.
