So, this is simple a two chamber soak tank with an inner basket for holding the parts.
Step 1: Materials and Tools
You'll need some sort of hole making capability, like a hand drill with some bits. I used 1/8" and 3/32" for this instructable, but it really depends on what you're going for.
To make a handle (totally optional but handy in the same spirit of "not getting black grease soup all over your hands") I used some 16ga. fencing wire. I have some snips and pliers to cut and shape the wire.
Step 2: Drill the Inner Basket
After using this for the first time, I would recommend putting more holes in the bottom and keep the side holes low. When you pick up the basket, you have to keep the side holes below the rim of the outer container. I originally chose to go for more side holes to try to keep small parts from getting lodged in the bottom, but if you go sufficiently small enough with your drill bit, you should be fine.
Step 3: Prepare Handle
Work the wire roughly into the shape of the inner container. Mark the rim of the container twice at the midpoint where you will drill holes for the handle. Mark the wire slightly to the inside of the marks on the container to give the handle some room to sit inside the lid.
Take the wire and bend out at the marks.
Step 4: Install Handle
Move the handle back and forth a few times. In one direction it will stand almost straight up (you can adjust the height of the handle eyelets to determine where it stands) and the other side will sit mostly within the rim, depending on how far down you drilled your handle holes. Once you're satisfied with the positioning, bend the wire around the handle once or twice and trim. Consider putting something to cover the end of those wires, like a bike cable end or melted wax or something.
Step 5: Test It Out
As I was writing this, I got the idea that you could maybe use scrap brake/derailleur cable to make the handle, and crimp it all together with a housing end.
I have been working on projects to reuse these types of containers since I don't seem to be able to recycle them in my area (the city of Raleigh, where I do most of my recycling, specifically says no wide mouthed containers like yogurt etc.) so maybe some of those other projects will make it here.
Hope this is helpful to someone.