My oldest daughter had a Winnie the Pooh smock-style bib when she was little. It died, as plastic bibs are wont to do. And when my little one started feeding herself more, I looked in vain for a similar model. I finally found one but it was very pink and covered with Disney Princesses, and while the little one loves princesses, this was a bit overpowering. So I decided to use it for a pattern to make my own bib.
To make this bib you will want a piece of fabric about 22" by 17" and a package of double fold bias tape. To protect from stains I would suggest laminated cotton or Therm-o-Web Iron-On Vinyl. Since Joann's and Hobby Lobby are my only local resources, I will be using the iron-on vinyl in this tutorial.
I prefer to start with heavy weight fabric with a cool pattern. Here is the pattern you need to cut out (with measurements):

After you cut out your bib, you should decide if you want to add a pocket to the bottom of the front. You could make this out of clear vinyl if you have it or another piece of your fabric. You just need to decide how deep a pocket you want.
If you don't have laminated cotton, you will now need to iron on your vinyl (sorry about the different color fabric, I have two bibs in progress).

Now you can start sewing the bias tape on. You will want to start by sewing it on the edges of the arms (and top of the pocket if you decided to add one):

Then you will start sewing bias tape on at the corner of the neck, and then down the arm. You will want to bring the two corners of the arm edge together in order to create your sleeve:


Continue on around the edge (attaching your pocket if you choose to add one), and finish your other sleeve, too:

Then you will want to leave some bias tape for a tie (being sure to sew it up first), then sew some on around the edge of the neck. You will obviously want to leave a tail on the other end too:

Due to the limited width of iron-on-vinyl, you cannot really make this pattern any wider than it is in the arms. If you have laminated cotton, you can make your sleeves any length you want.
Also, you might see that I used narrow bias tape. This was a mistake, as far as I'm concerned. It will work fine, but wider bias tape will go on easier and faster. And who doesn't love easier and faster?
Before you go off to create your own bib/smock, you should see it action of course:


Please let me know if I can clarify anything!