Gil Fronsdal has a good introduction to investigation that you can find here: Investigation
Santikaro, a western student and translator of the well-known Thai teacher Buddhadasa, has a detailed article on investigation that relates it to the practice of mindfulness of breathing. You can find that article here: The Investigation of What is Important
Tara Brach emphasizes the practice of investigation with kindness and care in her teaching of the meditation practice RAIN. You can find more on that approach to compassionate investigation, along with other resources on RAIN here: RAIN: A Practice of Radical Compassion
Anxiety is a major reason that many people find themselves interested in meditation. You can find a good discussion of anxiety and mindfulness from Leslie Booker in the following post, where she suggests that we can learn to befriend our anxiety through the practices of mindfulness and investigation: Making Friends with Anxiety