Bodhipaksa has a good article on self-compassion that includes several approaches we can include in our practice of self-compassion. As his title and the quote above suggests, he has found self-compassion practice to be one of the most important practices he’s encountered in his long history of meditation practice. You can find his article here: Self-compassion: Lovingkindness Squared
Kristin Neff is widely known for her teachings on self-compassion and practices that we can use to open ourselves to self-compassion. You can find an introduction to her approach to mindful self-compassion here: What is Self Compassion?
Tara Brach is best known for her teachings on the practice of RAIN, an acronym for an insight meditation practice that can be very helpful when we’re faced with difficult emotions. In this article from her website you can find some suggestions and resources from her on the relationship of the practice of RAIN to self-compassion: The RAIN of Self-compassion