For the somewhat more adventurous. Don't be intimidated by the length of this, I've been thorough. Read it through and then take it step by step.
Sewing is NOT difficult. Put aside all of your assumptions that only professionals can do this and have at it. It's what your grandmother would have done. ;-)
Take a bag that you already have, turn it inside out and look at its construction. Chances are it's either two rectangles sewn together or a very long thin rectangle folded in half. If it's folded there will be two seams, probably one up each side. If it's two separate pieces, there will be three. In both cases, the open end will be finished in some way - it's the part that gets the most wear. There may also be some way of closing the bag (like a drawstring, a tie or foldover flap).
These are the elements you need to incorporate. How you do that is up to you.
Materials needed: Fabric, scissors, ruler, thread, sewing machine or hand needle, flat surface to measure on.
Recommended: Pencil or sewing chalk, iron, belief in yourself. :-)
1) Lay out your fabric and place your toy on top of it. Try folding the fabric over it to get an idea of how it will work. The fold can be at the bottom or one side, whatever works. Or maybe two separate rectangles is the best use of that material.
For the sake of simplicity in writing, let's assume that you're working with two separate rectangle pieces. That means two side seams, a bottom seam and a finished edge at the top. (If you're not, adapt to suit.)
2) To figure out how wide to cut your material, take the desired finished width and add twice the width of your preferred seam. So (as an example) 5 inches + 1/4 inch + 1/4 inch = 5.5 inches.
To figure out how long to cut your material, take the desired finished length and add the width of your preferred seam. Then add an inch for the finished edge. (If you're dextrous it can be less, say 3/4 inch.) So (as an example) 10.5 inches + 1/4 inch (bottom seams) + 1 inch = 11.75 inches.
3) You'll need two rectangles with those dimensions. Flatten out the material again. Measure and mark your pieces. Pencil works or get some sewing chalk. (If you're nervous about sizing, draw the measurements for one piece and fold the material over to double it. Pin along your seams lines, pop your toy in and see if it works or if you need to change something.)
4) Cut your material. Decent sewing scissors make this much easier, so they're well worth the money if you're going to be making several bags.
5) Place your pieces together with the right sides facing each other. (The right side is the one you want showing.) Pin near the soon-to-be seams to keep them from moving around and driving you batty. :-) Stitch your seams. (Feel free to draw in a stitching/seam line as a guide if you want.)
You should have an inside out bag.
6) Turn down 1/2 inch on the top, open edge. Crease it along that fold with your fingers or iron it flat. Turn it down another 1/2 inch and crease or iron it again. Stitch along the bottom of that to hold it all in place.
7) Turn your bag right way out. Use a ruler or something flat but not sharp to poke the bottom corners out. Give it a nice press with an iron if you have one.
8) Pop your toy into the bag and gather the extra material together above it. Measure how much extra material there is. Take the toy out, smooth the bag and measure down from the top. Make a small pencil or chalk tick in the centre of the back side at that point or a bit higher. Fold a length of ribbon in half and sew on at your mark.
Put the toy back into the bag, tie the ribbon to close it up and you're finished.