Periodicity is not well defined term. For example, such data:
1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11, 1, 10, 1, 10, 1, 11
you may treat as one with not exact but strong periodicity of 2, and as exact periodicity of 6.
For exact periodicity you may simply try to find given data as substring of data repeated twice.
For non exact periodicity of real, noisy signal time domain and frequency domain methods may be used.
Time domain one is self correlation. It is like a substring search above: searched for a shift value on which data have maximum self similarity.
For simple signals counting threshold transitions may be enough.
Frequecy domain methods include one using FFT/FHT: search for a maximum in fequency spectre which gives 1/T of periodicity.
Another method is using Cepstrum.