Burp Cloths are essential to any new mother. So they make wonderful gifts or personal use. My kids are long past that stage with my youngest being 10. But I do need a gift every once in awhile.
This is how I make mine.....
Fabric choices..... this is critical IMHO.... When an urp happens something absorbent is needed NOW! Personally while cottons are cute and come in so many more cute prints, I don't use them for burp cloths or bibs. While they are absorbent they just aren't absorbent enough for either IMHO because they don't hold much for liquids. Instead for the front I use good ol' flannel.
The backing leaves a lot of choices, when my kids were little I use two layers of flannel and well I personally wasn't happy with them. I wanted more absorbency. So I don't do that anymore. For some recent gifts I use cotton terry (the stuff bath towels are made out of but found on the bolt, but towels would also work) and they were beautiful. But there are also some new great fabrics on the market that are still very absorbent but thinner, such as bamboo terry or bamboo fleece (not to be confused with polar fleece) While polar fleece is plush and cushy it's just not absorbent, in fact polar fleece is actually water resistant and repels liquids.
Then because I hate turning things inside out, and working hard to get my seams even and nice I cheat. I sew wrong sides together and cover the raw edges with double fold bias tape. You can buy this or make your own. I make my own and have the bias tape maker made by simplicity. Because I'm not going around any round edges I just cut strips with my rotary cutter, quilting ruler and cutting make. I can make them matching in a solid or print super fast and easy. http://www.amazon.com/Simplicity-Creative-Group-Inc-881925/dp/B002CT3YX2
Honestly I like the plain rectangle ones. My daughter when she was a baby had gurds so she spit up a LOT, and I wanted that extra neck protection. While the curved ones look cool, they don't provide a lot of protection where you may need it the most. I would rather not have spit up running down my neck and inside the collar of my top.
Last but not least..... SIZE......
I started with buying my prints in 3/8 yard cuts. Zigzag the raw edges before washing and fold as you would to make sure it's straight and even. Then simply cut it in half, so your 45" long is now half that and still 3/8 yard wide. I place my backing fabric on behind, wrong sides together and trim out as needed. Grant your burp cloths won't be exactly the same size but close enough. If your picky just cut them all out the same. You can cut both layers at the same time to save time. Pin sides together before lifting and I do a quick stitch around so they don't shift when I am sewing on the bias tape binding. Sew on bias tape using your favorite method. I like to sew it onto the back first (when I don't forget), and then onto the front so I make sure it looks really nice from the top. Sometimes I may use clear thread for the top for a nicer look.
For the bias tape binding I would suggest a cotton because you don't want the extra bulk of the flannel for the binding. You can use prints or cottons, however personally I usually use cheaper solid prints just to keep the cost down a tad since I am using the more expensive cotton terry for the backing and a nice flannel print for the front.
But either way they make nice burp cloths and after the baby is grown can be used as cleaning rags or whatever rags and will last a very long time because they are made well and very durable. There are so many cute flannel prints these days to take advantage of.
I've gotten a lot of compliments on these from the new mom's i have given them to.