Sampling is the process of taking a Continuous Time signal and representing it as a Discrete Time signal. This is advantageous because with computers and other digital devices we have no other way of representing an analog signal. The key to sampling is picking a good sampling rate. If you pick too low of a sampling rate you can loose a lot of data on your signal or if you pick too high a sampling rate, you are going to be storing more data than you need. The name associated with the the minimum sampling rate is the Nyquist Rate which is equal to two times the bandwidth. If your sampling rate is at or below the Nyquist Rate you run in the the phenomenon of aliasing. Once you have the DT signal and assuming that you have used a good sampling rate, you should be able to reconstruct the CT signal without much fuss.
