Take the spilt open gizzard and clean it in a bowl of water. Make sure to get all the grit out. DO NOT do this under the sink. It will clog your pipes very quickly. Also when you are done do not throw this water down the sink, just dump it in your backyard.
Split the gizzard in two now. Start trimming all the edges and silverskin material and anything that doesn't look like meat.
Repeat on the other half. Remove the silverskin. You can start by taking the tip of the knife cut some of the silverskin off and then peel it off. The gizzard should look like a roundish pink meat.
There are gizzard recipes throughout the web so find one that looks appealing. If you're worried about eating innards try a fried recipe to make it easier to start. I use the same marinade I use for ducks and cook it with the bird. If you have concerns remember a gizzard is just meat. It is harder but it does not have any gaminess or ironiness that other innards have, so it is an easy entry meat for the nasty bits. Textually though it is harder than flesh but its quite edible. Give it a shot.