The simplest solution is to use Full Information Maximum Likelihood (FIML). You just need to specify FIML as your estimation method.
The other options are to use multiple imputation if you want a better guide on filling in missing variables. You will need good predictors of the missing variable though.
I think, data screening is better prior to run SEM. You can fill missing values of continuous variables by Mean of the variables, and the value of Mode can be use to fill the categorical variables. I hope this might be helpful.
This is critical in the case of regression and path models and you will be prompted to inform you that estimates cannot be obtained due to missing values.
in AMOS for example you will get suggested alternative estimation methods (such as those suggested by Andy above) as a prompt. In the case of regression this alternative may be of limited effectiveness in analysis
in many regression processes analysts frequently collapse/conflate IV or DV and even if codes for missing values are present when collapsed/conflated missing data reappears
this is not so critical for factor analysis - but still good practice not to have
it depends on the level of missing data you have, I think it sometimes better to pre-screen out the missing data (but only if sample size integrity is maintained).