I start with my outfits. I particularly like having scarves that will tie colours together, so many of my scarves are prints. A taupe jacket with a blue chambray blouse looks weird to me, for example. Until I add a scarf that has both those colours and then magic is made.
Alternately, I like to have a few solids on hand to go with prints.
Probably best to start with silk square scarves or longer rectangular ones. I find these are the ones I reach for the most often, because they are so versatile. Choose colours that are frequent in your wardrobe. Start looking at yourself in the mirror and asking "What kind/colour of scarf would go well with this?" When the same answer keeps popping up, that's what you have to look for. I have my eyes open now for a scarf that combines rust, black, and white, because that's a colour combo I'm in love with right now.