This is pretty simple. Cut the crown off of the broccoli and do with them as you please. I blanch mine and keep them in the fridge for a week of awesomeness. Cut the bottom 1/8-1/4 inch off the stem.
With a knife and/or peeler, remove the fibrous outer layer. the bottom of the stem is the most fibrous and as you get closer to the top, it's easier to digest. Spiral slice those stems! I had to cut mine in half to fit them on the spiral slicer. The top half where the crowns come off should be upright or they'll split apart. I used the widest blade attachment because I like linguini rather than spaghetti.
With the finished product, saute as you would zucchini linguini (or "zoodles" as some people call them. Does that make these "broodles") and serve with whatever sauce you like. Or you can eat this raw if you want