Steps for scanning regression tables

This is a typical, if simple, regression table for an ordinary least squares regression (OLS).

The steps required to understand it are summarized below, with fuller explanations in the next sections.

Step 0: Substantive Meaning

Know what the variables mean and what the unit of observation is. In the table above, the variables are the % shift to Trump and county median income. The unit of observation is one county in the United States.

Step 1: Statistical Significance

Identify coefficients with a star. In the table above, $-0.158$ is a coefficient. For the OLS regression with one variable presented above, $-0.158$ represents the slope in the single variable linear equation. In other types of regressions, a coefficient is similar to a slope, but not identical to one.
The star is a very approximate indicator of coefficients that are worth paying attention to. These are called statistically significant coefficients.

Step 2: Direction of the Effect

Look at the direction of the coefficient/slope. Is it positive or negative?
We can only be confident in the direction of the effect if the coefficient is statistically significant.

Step 3: Substantive Significance/Effect Size

Substantive significance indicates whether we care about the size of the effect/coefficient. It is not the same as statistical significance, and is at least as important as statistical significance.
The coefficient $-0.158$ indicates our best guess about the effect size. This can be translated into an indication of substantive significance, but is never more than a best guess.
The next sections describe how to interpret coefficients in linear regressions. For other regressions, rely on the author to interpret the substantive meaning of the reported coefficients.