As Florent points out, there are several different ways that different people define validity. One of the simplest (conceptually) is discussed in the linked publication. Testing it could be done by conducting an experiment in which you manipulate what you are trying to measure.

Article The Concept of Validity

As Florent points out, there are several different ways that different people define validity. One of the simplest (conceptually) is discussed in the linked publication. Testing it could be done by conducting an experiment in which you manipulate what you are trying to measure.

Article The Concept of Validity

With regard to reliability, the most commonly used statistic is Cronbach's alpha, and there have been so many questions about that topic that I have complied a set of resources:

https://www.researchgate.net/post/How_can_one_help_people_create_simple_scales_from_Likert-scored_items

Here are examples of actual statistical calculations for reliability and validity

https://www.researchgate.net/publication/282074208_Statistical_Applications_on_Validity_and_Reliability

Research Statistical Applications on Validity and Reliability