Question

how can we reconstruct a signal from its samples???

Answer 1

First and foremost the Nyquest(?) criteria of a sampling rate greater than twice the maximum frequency under consideration.

Answer 2

reconstructing an analog signal from the digital domain works by using a reconstruction filter which is basically a digital to analog converter (DAC). In a DAC, very briefly, there's a preset value which is the digital counterpart of a mean analog value. The incoming digital value is compared with this digital counterpart of the mean value and the output analog signal is either increased or decreased based on the comparison.
Now, the output of this DAC is stepped ie there are voltage steps instead of a smooth signal. So we use a low pass filter after the DAC which removes the high frequency components and smooths the stepped signal.
In the digital domain, one needs to be specially aware of the Nyquist Criterion, which says that an analog signal can be recovered from its digital counterpart without any losses provided the sampling frequency of the digital signal is 2 times the highest frequency component of the analog signal. If this criterion is not satisfied, we reconstruct a wrong signal (yes, the signal will be reconstructed).