Yes, looking at your competitions keywords is a very good start
You can do this by typing into Google different keywords phrases, for example if you live in New York do a search like this:
"Cleaning services in New York" Or "Cleaning companies in New York".. Or "Office cleaning services in New York". Just get creative and try a whole bunch!
If you are a residential cleaning company, also don't forget: "Maid Services in New York" , "House Cleaning Services in New York" I hope you get the picture