  The main goal of this paper is to give a complete proof of the trace theorem
for Besov-type spaces of generalized smoothness associated with complete
Bernstein functions satisfying certain scaling conditions on $d$-sets
$D\subset\mathbb R^n$, $d\leq n$. The proof closely follows the classical
approach by Jonsson and Wallin and the trace theorem for classical Besov
spaces. Here, the trace space is defined by means of differences. When $d=n$,
as an application of the trace theorem, we give a condition under which the
test functions $C_c^\infty(D)$ are dense in the trace space on $D$.
