This site:
http://www.wikihow.com/Sew-a-Patch-on-a-Uniform
has a very good basic explanation for it.
A few warnings, before you start - if the backpack is waterproof, the stitching will create leaks where the patch is located. You can use seam sealer or seam tape to reseal your pack after you put the patch on.
Fusible web (essentially iron-on tape that can be found at most fabric stores) works very well, and you can use an iron to attach it, saving all the hassle of trying to sew it. Be careful, though - synthetic materials are heat-sensitive, and your pack may not withstand the heat needed to iron the patch on. (you can bring the pack into the fabric store and ask the clerk there for advice)
They also make fabric glue:
http://www.save-on-crafts.com/oktowash1.html
This may be the best solution for the item - saving the wear and tear of trying to sew, worrying about damaging your pack or melting it with the iron...
I know that the same brands aren't available everywhere, but these products are sold worldwide (and, for that matter, a good silicone adhesive would probably do the trick, bond stronger, and is guaranteed waterproof)