My first starting point would be to review plot descriptions, under Plot output on page 853 of the Phoenix 1.3 User's Guide.pdf (or equivalent in whatever version you are using.
Beyond the starter suggestions e.g.
Pop CWRES vs IVAR
Plot of CWRES (conditional weighted residuals), a recently proposed replacement for the classical WRES (weighted residuals) goodness of fit statistic, against IVAR, the independent variable (typically IVAR is time in a PK fit, concentration or dose in a PD fit).
Values of CWRES should be approximately N(0,1) and hence concentrated between y=-2 and y=+2. Values significantly above 3 or below -3 are suspect and may indicate a lack of fit and/or model misspecification.
Some references are given for further explanation and back ground reading e.g.
A. C. Hooker, C. E. Staatz, and M. O. Karlsson (2007). Conditional Weighted Residuals
(CWRES): A Model Diagnostic for the FOCE Method, Pharmaceutical Research,
Ultimately it does come down to a combination of understanding, expertise and experience, I am sure other readers of this forum can propose their own tips and suggested reading.
For Covariates, try following the example in Chapter 10 "Covariate Modelling" of the NLME Examples guide and seeing how the plots changes as covariates are added to the model. Also if you have a specific project you would like to post as an example then we can perhaps try to work through that.
A CWRES vs Time plot showing the parallel LOESS fits indicating relatively even error over the whole time range