Install the docs package to obtain man pages.
apk add docs
The docs special package installs docs for both already installed
packages and future ones automatically.
Busybox itself has a man page (man busybox) which only has a terse
overview of the utilities. For more detailed documentation, the
opengroup specs are handy (busybox tries to, but does not guarantee,
POSIX conformance).
But hey, there is a better way!
apk add man-pages-posix
Or maybe it is time to move on to coreutils so that the tools themselves come with their corresponding man pages; pages, that reflect the reality of their implementation.