Set up the measurement model in the appropriate software and run the analysis. From the output, assess the goodness of fit between the model and data using indices such as the chi-square index, which should be close to zero, the root mean square error of approximation, which should be less than 0.05, and the normed fit index, non-normed fit Index and the comparative fit index, which should all be greater than 0.9. Not meeting these criteria indicates a poor fit between the model and the data. Professor David Kenny of the University of Connecticut provides a summary of commonly used fit indices in the link in References.
Verify that the loading of each measured variable on its underlying factor is significant in the manifest variable equations and the standard errors are not near zero. If a loading is insignificant, the variable can be dropped when modifying the model, if such a change is consistent with the theory.
Verify that the residual matrix entries are close to zero and the distribution of normalized residuals is symmetrical around zero with few large residuals. If not, the model may need to be modified consistent with the underlying theory.
Determine that all possible pairs of factors in the research model are distinct from each other by comparing the chi-square fit index of the research model with the chi-square fit index of an alternative model in which the correlation between the pair of factors is set to 1. The better model is the one with the lower chi-square index.
Review the modification indices in the model. First, examine the Wald Test results in the output to identify parameters that can be dropped without increasing the model chi-square significantly. Next examine the Lagrange multiplier test in the output to identify if new factor loadings or covariances should be added to the model.
Modify the measurement model remaining consistent with the underlying theory and run the analysis again.