The first thing I’d do is a visual analysis. That helps to understand what data you are dealing with.
Secondly, (if its still not clear), stationarity tests.
If it is stationary (i.e. its just a noise) you dont have much options - just measure mean/std etc.
If it is not, in addition to basic statistics I would check seasonality and trend (check seasonal decomposition), auto-correlation, how well I can approximate it (try different functions), Fourier analysis is an option as well.
Also it’s possible to try all that with log-s or diff-s.
It all depends on the result you expect, in the common case I’d start with the stuff above.