Scarves are a signature part of my style, though I don't always feel the love for them that statement would imply! The thing is -- I often want interest or colour near the face, I don't much care for wearing necklaces, and through the early spring/ fall/ winter months, I always want the added warmth on my neck if I am not wearing a high collared buttoned up shirt or a turtleneck top! This is related to my short hairstyle and my longer neck, of course.
How I wear them depends on the type of scarf and reason for wearing. OUTDOOR scarves (worn for warmth with a coat, to be taken off indoors, frequently knitted or wool or other cozy fabric) I often wear with a Euro knot. Especially if they are long and oblong or rectangular in shape. I also own an infinity knitted scarf that is fun to throw on like a shawl, and two much larger winter scarves that are shawl-like.
Scarves for indoors I tend to wear as Janet describes, especially if they are the large squares. I'm rarely knot them unless I need to hold them more secure and if I do, I often hide the knotted part underneath the rest instead of letting it show. Longer lightweight oblongs or rectangles I will loop in a Euro knot or just loosely wrap around. Sometimes if the fabric is especially light, I'll experiment with some other kind of knotting technique.
I have never worn the small squares well. I own a few but rarely enjoy wearing them because for me the fuss factor is too high. I can't get them to stay put or look relaxed enough on me. (Which sounds like an oxymoron and possibly is, LOL) I think I could like these if I figured out a styling strategy that worked.