To remove the solenoid from the carburetor you'll first want to disconnect the negative cable from the battery. I cannot stress this enough. If you don't when plugging/unplugging the solenoid there could be a spark. The very last think you want at the bottom of the carb is a spark. I've seen it happen first hand and the outcome is not pleasant.
Once you have the negative cable removed from the battery you can take a 1/2" wrench and that may slip onto the top of the solenoid. I say "may" because it may not. Most wrenches have to be ground down to make them thin enough to fit into the slot. However, some do not and will work just fine. If you don't have a wrench that is thin enough to fit, you can used some needle nose pliers. Also, if all else fails, you can grab the blow and twist is counterclockwise and sometimes that will loosen the whole thing. I generally don't recommend doing that as it can damage the o ring on the bowl base.
Your assessment that the float sticking is causing your problem is more than likely going to be correct. The only other thing that can really cause that would be if the key is being left on, which would cause the solenoid to not turn off. Or, if the solenoid is stuck "open", which can happen.