According to the eigenvalue criterion, only components with eigenvalues greater than 1 should be selected. each component should explain at least one variable's worth of the variability

The proportion of variance explained criterion states that the components should be selected one by one until the desired proportion of variability explained is attained.

The minimum communality criterion states that enough components should be extracted so that the communalities for each of these variables exceeds a certain threshold (e.g., 50%).

The scree plot criterion is this: The maximum number of components that should be extracted is just prior to where the plot begins to straighten out into a horizontal line.