What some people do is to rent space in malls or similar shopping areas and set up tables from which they are able to greet people and present their products and opportunities. I have seen this done for cosmetics, health supplements, and other products and services. Sometimes it works well, but there is a cost involved most of the time, but some mall managers will give you a break if you are just getting started, since this also can add to the shopping environment in the mall.
You can try various stores and businesses to see if you can leave your cards there for people to see and take.
You could also do visiting demonstrations. For example at a hair salon or daycare center or even an office-type business you could schedule "shows" for the staff and customers. You may need to offer something to the businesses in exchange for the privilege, but it can certainly be productive.
Ads on bulletin boards can help--supermarkets, laundromats, etc.
There is, of course, the old stand-by, door-to-door selling. Surely you have heard, "Avon calling."
If there are fairs or flea markets in your area, those can be good places to set up, too.
Some folks put flyers on windshields in parking lots, but I have never taken well to that method, and I suspect many people will either be irritated or at best disinterested.
Some towns allow occasional street vending from a temporary booth or by carrying a sample kit with you and greeting people as you encounter them. You should get proper permits if you decide to try this, but I am not convinced it is right for the Avon image. You can decide that, though.
There are the party methods, too, such as are used by Tupperware and other products.
Well, let's see what others have for you. Good question.