The website Mindful.org has a good introduction to mindfulness from a secular perspective, with basic information on what mindfulness is, plus many suggestions and guided meditations for learning to practice mindfulness, both formally and in daily life. You can find their article here: Getting Started with Mindfulness
Phillip Moffitt provides a helpful introduction to mindfulness that looks at the ethical and philosophical orientation of the Buddhist practice of mindfulness. In either Buddhist practice or the secular practice of mindfulness, the relief of suffering is one of the main motivations for the practice of mindfulness. You can find Moffitt’s article here: What is the Mindfulness of the Buddha?