Here is the cardboard letter I picked up Joann Fabrics:
First I painted the entire letter with white craft paint. I took my several coats to get a solid application with none of the brown peeking through. Next, I used those little round office stickers (What are they used for anyway? Mine were left over from a garage sale.) and covered the letter like so:
My end goal was to have polka dots, but I knew I wouldn't be able to paint them on perfectly, so I used these dots to achieve the look I wanted. Also, since I wanted white polka dots on a blue background, I thought painting the letter blue first and then painting white dots wouldn't work out too well: I would need to do multiple coats of the white to cover the blue, which only increased my chances of messing up my dots. There may have been an easier way to do this, but I didn't know of one.
Once I had my dots attached, I used pale blue craft paint that I already owned to cover the S. I only did one coat, but applied it very thick. As I worked my way down the letter, I removed the stickers as I went. I simply painted over each sticker then made sure my fingers were clean and peeled the circle off.
I was really happy with the end result: