Does anyone on this board have any idea on how I can breathe INTO a movement, to make that movement more fluid, relaxed. Also, how I can breathe to sink the chi into my dantiem area (lower belly) -- or is the actual goal to sink the chi down into the floor, past your feet?) What can I say, I'm a Tai Chi newbie, lol.
Unless you're being directed in a particular such practice by your teacher I wouldn't concern yourself with breathing "into" a movement. Just breath easily/naturally-at this time if it helps you can intentionally work on relaxing unneeded tension in your movement as you exhale-but just exhale normally,try not to put anything extra into the exhalation. For a simple "sinking" into the dan t'ien just practice feeling the area as you inhale/exhale and think of your breath sinking to it on exhalation. Try this when not moving for awhile first. Past your feet? If someone's not teaching this type of thing to you I'd leave it alone at this time. This is mostly pretty simple stuff. Asked your instructor?
All movements in a form are in a cycle of yin (contraction) and yang (expansion), which correlates to your inhalation and exhalation respectively. During inhalation, your 'breath' or 'qi' should be expanded outwards towards your extremities from your dantian, and during exhalation, back towards your dantian and down to your root. You will first need to learn to regulate your abdominal breathing smoothly and this should translate into your fluidity of movement if you can visualize your body as a human balloon, and all your movements are expressions of your 'qi'.
If you want softness, relaxation, and eventually more power... it sounds like breathing into a movement is what I've been taught as "leading with the breath." For example, raise your hand as you inhale. Start your exhale a moment before you lower your hand. Start your inhale a moment before you raise you hand. So the direction of breathing changes just a moment before your body changes direction. This is leading with the breath. This is different than changing direction of the hand and changing direction breathing at the same time, which is much more tense and rigid.