In this paper by Dwyer, Greenlees and Iyengar, we are introduced to symmetric spectra, and more particularly to the notion of an $\mathbb{S}$-algebra.
In both the Notation and terminology ($1.5$), and Rings and DGAs vs. $\mathbb{S}$-algebras ($2.17$) sections, it is said that we can convert any ring $R$ into an $\mathbb{S}$-algebra.
The procedure for turning a (unbounded) chain complex into an $\mathbb{S}$-algebra is touched on in Section $2.6$, but not the case of a ring.
How do we go from a ring $R$ to an $\mathbb{S}$-algebra? Specifically, do we assume that a ring is a DGA concentrated in degree zero?
EDIT: Another candidate, as suggested in the comments by William, is to let $HR$ be the Eilenberg-Maclane spectrum for the underlying abelian group of $R$.