  We investigate the existence of solutions to the fractional nonlinear
Schr\"{o}dinger equation $(-\Delta)^s u = f(u)$ with prescribed $L^2$-norm
$\int_{\mathbb{R}^N} |u|^2 \, dx =m$ in the Sobolev space $H^s(\mathbb{R}^N)$.
Under fairly general assumptions on the nonlinearity $f$, we prove the
existence of a ground state solution and a multiplicity result in the radially
symmetric case.
