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To view an article from Tablet.com with a full list of menorah cleaning suggestions, click here.  

Sample suggestions:
Freeze your menorah, “and the wax pops right out.” 

“I fill the sink with HOT water, then let the menorahs sit submerged. After a minute or two, I pull the menorah out and use a paper towel to wipe off any remaining wax that hasn’t melted and floated to the top of the water in the sink. I then user the paper towel to skim the floating wax.” 

Similarly, you can “take the menorah outside and pour hot water on it to melt off the wax. It’s easier to clean up outside than in the sink.” 

But: Safety first. Wear oven mitts and make sure the Hannukiah can handle hot temperatures

And here is an alternate suggestion from Barry Glovetsky: “You DON’T remove it, except for the minimum needed to insert candles the next time. Every drop of wax is a memory.”