Repairing a cut crocheted item.  I'm asuming it's double crochet.  First, I took a few rows of dc and cut the middle of it, as if a child had done so:



Second, I unraveled all I could, making sure to obtain a nice hole where I could work in, and also taking away all the bits.  Try to get some nice long tails that you can later on weave in.  I found a loop to begin my work with:
 

Then, put your hook thru the two hanging loops of the upstairs double crochets (smiles!), yarn over with your new yarn, and start your double crochet.  You'll finish it by pulling the new yarn thru ALL of the loops you started with.  It *will* look as if you had made a mistake and worked behind the double crochets, but if you use the same yarn, I don't think it will be so noticeable:



Continue to the end, and then leave a long end for weaving in.  When you weave in, you will need to tack your new double crochets to the one next to it on the left (or right, if you're a lefty).  Turn your work and start again with a new piece of yarn.

Now I'm going to show you what the work looks like with white yarn:



I'm sure that if you crochet more loosely than I did, that you're work will be better than mine.  I think the trick here is to make sure you unravel enough yarn all around in the piece so that you will be able to weave it in.  Also, remember that you will need to tack your new work to the old, so weave in the ends carefully so a hole won't show because you forgot to tack it!

:o)

God bless you!

Ambar Enid
"Trust in the Lord with all your heart
And lean not on your own understanding;
In all your ways acknowledge Him, and He shall direct your paths..."