There are a ton of tutorials floating around the Internet for this type of project so I won't bore you with too many photos but I will provide you with dimensions that I find practical.
I cut two pieces of flannelette 27 x 10.5 inches. On the white lining of my burp cloths you'll notice that I have sewn in a third piece of flannelette down the center for extra absorption. This center panel is cut to 19 x 4.5 inches. On my burp cloths I used a white lining but feel free to use any flannelette you'd like.
To begin construction, simply iron down a quarter inch seam allowance along the entire center panel and pin it into the middle of one of your burp cloth pieces (tucking the seam allowance under and out of sight). I used a simple zigzag stitch to adhere it to my burp cloth but feel free to use a fancy stitch if your machine has the capacity and you have the extra time.
Now that you are down to two flannelette pieces, pin the fabric right sides together. Sew around the edges using a quarter inch seam allowance but be sure to leave a 3-4 inch gap at one end. Using the gap you left open, turn the burp cloth right side out and use a chopstick to push out the corners. Press the cloth flat using a gentle iron, and sew along the perimeter of the burp cloth (close to the edge to ensure you catch the seam allowance that is folded inside).
These make a cute and simple gift that can be tailored to anyone's style. I think my massage therapist will love them.