I am a certified mindfulness meditation instructor (15 years) and senor practitioner (20 years) in the Tibetan Buddhist tradition, with experience in the Zen tradition as well. All you need to remember in beginning practice is to keep it simple, and with a light-touch. There are endless techniques from simple breath-focused meditation to very complex, shamanistic ritual meditations such as the Tibetan Buddhist Chod tradition. The point is...all the practices start with observing the self, the emotions, thoughts, behaviors, environment etc. From what I understand, Linehan incorporated mindfulness practice into her therapy because it helped people who have emotional deregulation, that is, the inability to regulate extreme emotion. But mindfulness meditation practice is also good for dysthymia, even though it is very different than deregulation.
Whatever practice you are given I would say follow this one piece of advice: Don't force it. You can't force yourself to relax. But if you accept whatever emotional state you are in, then gradually and naturally you begin to relax. The biggest mistake beginners make is to push too hard. For depression the antidote is to keep things as light as possible. That's why walking meditation is good - because it gets one outside. You didn't really say what techniques you were doing. All you need to remember is keep it simple, simple, simple -- yet focused. That is the discipline..to keep coming back to the present. Good Luck. PS I hope the program incorporates sensate focus exercises...that is...the sensations. So you would do something like eat an orange mindfully, or burn incense, or introduce something colorful and stimulating in your environment, like a piece of art. I think these would be particularly helpful for dysthymia.