There are methods to accurately estimate the variance components, corrected for a number of systematic effects. These variance components can be used to calculate the heritability. Potential issue is that for accurate estimates of the variance components a rather large number of records (animals with observations and pedigree) are required. If you only have a limited number of observations, or you don’t have good pedigree on the animals, there is a ‘quick and dirty’ way to get an impression of the size of the heritability: the parent-offspring regression. Parents pass half of their genes on to the offspring. If the trait you are considering is determined by genetics only, you would expect a regression coefficient of 1 if you would plot the average performance of both parents (also called the mid-parent) on the x-axe against the performance of the offspring on the y-axe. If the trait is influenced by the environment to some extent, but also by genetics, then you expect a regression coefficient smaller than 1, but larger than 0. This regression coefficient is an indicator of how much parents and offspring are alike. And the assumption is that the only factor that makes them alike is their common genetic background. In other words: the regression coefficient reflects the heritability. In some situations you will not have observations on both parents, but only on one parent. For example in case of a trait that only comes to expression in either males or females. In that case the regression coefficient does not reflect the complete heritability, but only half of it.
In Figure 4 you see an example of regression of the height at the withers of a number of Arabian horses on the average of their parents. The estimated regression coefficient, so the heritability, is 0.64. The estimated intercept of 0.56 suggests that the parents are systematically larger than the offspring. That could be a sign of a change in environment between both generations. This may be the case if the data was collected on one stud farm. However, it could also be a matter of inaccuracy of measuring the height at withers. It has no value in explaining the results.
It is important to keep in mind that this is not an accurate way of determining the heritability. If some families, for example, were kept in an optimal environment and others were kept in a poor environment, this will have influenced the results and will have an increasing effect on the regression coefficient, and thus the heritability. Similarly, if parents are kept in environments of very different quality to that of their offspring, there will be less relation between performance in parents and offspring and the regression will be low. Fortunately there are statistical techniques to take these systematic environmental influences into account.