Gather your cotton fabrics and cut squares using a template made of paper.

My squares measure 14x14cm, including 1cm seam allowance - I've made 11 aquares, so the finished scarf will measure 12x132cm.

Sew the squares onto each other to make a long stripe (or scraf, that is ^^)

Press the seam allowances like in the picture (I'd be grateful if someone could tell me the right English phrase for this ^^)

Now it's time to fold the seam allowances and press them like you'd do if you made hems.

Pin the scarf to the fleece, make sure it's as even as possible.

Stitch the edges.

Cut the fleece, leaving a small border (~5mm) around the scarf.
Don't worry, fleece fabrics won't fray.

And you're done!