Excellent pictures - that makes the discussion way more useful.
First, holding the carburetor the right way up, gently raise and lower the float (the hollow brass toroidal thing at the bottom). Look near the pivot: you will see the needle (a brass object clipped to the float's pivot arm) going up and down with the arm. We need to inspect where the invisible pointy bit on the top of the needle, seals against the carburetor body (the tiny toroidal part where it seals is called the seat). Turn the carburetor upside down, slide out the float pivot, and lift off the float. The needle should be clipped to it, so it will come out simultaneously. Now you can look at the seat, and clean out the passage to the fuel line. Inspect the seat for any dirt or damage (corrosion, scratches, or being installed crooked). Look at the part of the needle that seals against the seat. Look at the float: does it rattle or splash when you shake it? Is there any sign of a leak in the solder joint around it? When all is well, reassemble the float and needle. Hold the carburetor upside-down, so the float is in the 'up' position: is it parallel to the carburetor body? If it is, all is well. If not, tell me and I'll explain how to correct it. Do not try to correct it by just pushing on the float - that will mess it up.
Now it's time to clean out the rusty float bowl. Was the engine running properly aside from the flooding? If so, you can now reassemble the carburetor.
