What is the best way (most common) to discover if a stock is trending or not? (Despite drawing a line). A hurst exponent? A linear regression maybe?
See the average directional movement index (ADX):-
"At its most basic the Average Directional Index (ADX) can be used to determine if a security is trending or not."
It's easy to calculate. There is an example spreadsheet on the link page.
As in the answer by Chris Degen, various technical indicators for trend estimation exist (just to mention one additional: the moving average and moving average cross over).
In this free ebook by Rob Hyndman and George Athanasopoulos present various time series techniques for forecasting. These are ARIMA models and exponential smoothing methods. They can be used to estimate a trend in time series.
But be careful if I remember correctly then they state that stock prices are hard to forecast (if not impossible).