Practical process

1. Inspect plot. If mean-variance relationship, use variance stabilising transformation if necessary: square root (for count data, or mild relationship) or log (for strong relationship)
2. If clearly non-stationary difference, otherwise inspect ACF for very slow decay. Difference until this is gone. Check at seasonal intervals as well
3. Plot ACF and PACF for differenced series. Identify as AR, MA, or ARMA. If AR or MA get p or q from cutoff. Check seasonal lags as well. In ARMA first try p=1 and q=1.
4. Estimate parameters.
5. If any non-significant reduce model and estimate again.
6. Plot diagnostics (if data is seasonal make sure to extend for multiple seasonal lags). If problems try adding extra terms to model.