Let me summarise what Hilbert says in his *Zahlbericht* about the behaviour of rational primes in the cyclotomic field $\mathbb{Q}(\zeta)$, where $\zeta$ is a primitive $l$-th root of $1$ and $l$ is an odd prime.  You can read the orginial at the [Göttingen][1] site or a French translation at the [Grenoble][2] site.

Satz 117.  The ideal $\mathfrak{l}=(1-\zeta)\mathbb{Z}[\zeta]$ is prime (of residual degree 1), and $l\mathbb{Z}[\zeta]=\mathfrak{l}^{l-1}$.

Satz 118.  The discriminant of the field $\mathbb{Q}(\zeta)$ is $(-1)^{(l-1)/2}l^{l-2}$.

Satz 119.  If $p\neq l$ is a rational prime,  $f>0$ the smallest exponent such that $p^f\equiv1\pmod l$, and $e$ is defined by $ef=l-1$, then we have
$$p\mathbb{Z}[\zeta]=\mathfrak{p}_1\ldots\mathfrak{p}_e$$
where the $\mathfrak{p}_i$ are distinct prime ideals of residual degree $f$.

These results go back to Kummer (1847).  All this was much before anyone dreamt of Class Field Theory.




  [1]: http://gdz.sub.uni-goettingen.de/
  [2]: http://www.numdam.org/