Since no one more knowledgeable has jumped in on this one, I'll give it a shot.
I think this is what the pattern is saying:
Once you have the stitches on a needle, from the wrong side put your crochet through the first loop on the needle. Then put your hook through the middle of the purse handle (is it circular?) and hook the working yarn (which I assume is attached somewhere) and pull it through the handle. Now you've got the loop from the yarn that's gone around the handle and the original stitch from your needle on your crochet hook. Wrap the working yarn around the handle again, catch it with the hook, and pull that through both those loops.
I think the confusion might be that they never told you to insert your hook in that stitch on your needle -- probably because once you get done with those stitches, you're going to keep going around the purse handle till you have it covered.
What you'll end up with is a cover of yarn over the purse handle, which will be attached at the stitches you started with.
Hope this helps. If anyone can explain it better, or wants to tell me how wrong I got it, jump in!