The usual scenario is where you want to find if the received signal is noise: $$r(t)=n(t),$$ or if it is a signal plus noise: $$r(t)=s(t)+n(t).$$ It is generally assumed that you know $s(t)$. For example, you could have a radar application where you transmit a pulse and need to find if it was reflected back; or a digital communications receiver, where you want to see if the signal received was $p(t)$ (say, indicating a bit 0) or $q(t)$ (a bit 1).
The way to do this is by calculating the correlation between $r(t)$ and $s(t)$. The idea is that if the signal is present, you have
\begin{align}
\text{corr}(r(t),s(t)) &= \text{corr}(s(t)+n(t),s(t))\\
&=\text{corr}(s(t),s(t))+\text{corr}(s(t),n(t))
\end{align}
which is large. If the signal is not present, then the correlation is small.
This scheme also works in the digital domain, assuming that you sample fast enough. In general you want to calculate the correlation of a large number of samples, so that (by the law of large numbers) the probability of being unlucky and getting "bad" noise samples is small.
In your question, you don't say if you know what the signal is. If you don't, but you know some of its properties, you may be able to look for it. For instance, if the noise is zero mean and the signal is not; or if you know that the signal's energy is concentrated in a certain band (the noise is flat). However, a specific answer is impossible without more information.
If you don't know anything about the signal, detecting it may well be impossible.
