Time period of a signal is the time it requires to come back to its starting/original position after completing one cycle. There are two fundamental ways to calulating the time period of a signal or any system.
First, you could look at the waveform on a 2D graph with x-axis as the time axis and y-axis as the amplitude axis. So if the signal starts at zero and is a sinusoidal signal, then its time period would be when if crosses zero three time.
Second, Like Hazeem mentioned, Time period is the inverse of the frequency, which physically makes sense as frequency is the number of occurances/repetations (How many times does it repeats) of a signal in unit time, hence we can take the reciprocal.