Most cleaning services start as home-based businesses. A cleaning service, or maid service, can be either residential or commercial cleaning services, or both. They can have one employee, or several cleaners while the owner takes care of the business administration duties.
Advertising can be done by running ads in your local paper, business cards, printing flyers, posting on the bulletin boards of various businesses, and websites that provide local information and classifieds.
But by far, your best advertising will be from past and present customers who are very happy with your excellent customer service and the job you've done well.