I used to have a self-soothing kit when I was in DBT. It's basically using the five senses to calm you down. So having a soft blanket, a piece of your favorite food, a candle in a scent that you like, etc. are means to self-soothe.

Compassion to me is being more nurturing with myself, especially during those times that normally make me cringe, feel anxious, or feel guilty. I remember that I do have an illness and that sometimes I do things that are out of control. It's not me, it's the illness that I have. It helps reframe things that I did or have happen to me. It makes me more caring for myself, that I am human and slip up and that's okay.