Sampling a continuous-time signal means applying the general sampling idea along the time axis.

For sampling period $T_s$, measurements are taken at times $nT_s$, giving the discrete-time sequence

$$x[n]=x(nT_s).$$

The sampling frequency is

$$f_s=\frac{1}{T_s}.$$

A smaller sampling period places measurements closer together in time. Whether those samples are sufficient to reconstruct the original waveform depends on how rapidly the signal varies; taking many samples is not by itself a guarantee for an arbitrary signal.

Time sampling is distinct from quantization. Sampling chooses when the signal is measured, while quantization restricts each measured amplitude to one of a discrete set of values.

For sinusoids, sampling too slowly can make different continuous frequencies produce the same sample sequence. The general phenomenon is aliasing; the Nyquist-Shannon theorem gives a precise reconstruction condition for band-limited signals.