We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence ${\left\{{\psi }_k\right\}}_{k\in \mathbb{Z}}$ such that $\{{\psi }_k;k\in \mathbb{Z}\}=X$ and ${\psi }_k={\psi }_{k+lq\left(k\right)}$, $l\in \mathbb{Z}$ for all $k$ and some $q\left(k\right)\in \mathbb{N}$ which depends on $k$.