As Gaël mentions, assessing scale validity is a large and complex topic.
Here are just some basic suggestions to get you started:
- Check the factor structure of the test to evaluate whether items load most on the theorised scales. You could start with exploratory factor analysis and then later on build up to confirmatory factor analysis.
- Assess the reliability of the test given that reliability is necessary but not sufficient for validity. I.e., measure internal consistency reliability and test-retest reliabilility.
- Correlate your scales with a wide range of other variables.
- Do your measures correlate with other existing measures of the same construct?
- Do your measures not correlate or correlate to a lesser extent with things that theoretically should not correlate with the variable?
- Do your measures predict theoretically relevant and important variables?
- Do your measures correlate with alternative ways of measuring the variable (e.g., other report, behavioural measures, etc.)?
- Assess whether experts in the domain consider the items to accurately and adequately reflect the domain.
Acquiring this information typically takes multiple studies.
Furthermore, you may find it useful to think of validity as a property of the application of a test to the formation of a conclusion, rather than being a property of the test per se. Thus, you may want to reframe your question as one of saying whether the conclusions you want to make from the test are valid.