Hello Ashley,
Is it a good idea to establish where the papers will be distributed before trying to sell the ads?
You will definitely want to setup all your distribution locations first, before selling the ads. Companies will want to know where their ads will be seen. Having a list in your promotional package will add credibility to you and your business.
How do you go about convincing the establishments to carry the newsletter? Do you just walk in and ask them if you can distribute your newsletter there, or do you call them?
You can find a more detailed explanation of everything to do with Distribution locations here:
www.laughablenews.com/Distribution-areas/ (You'll need to be logged in to view)
But, for a short answer, yes you just walk in and ask (Don't call - for the reasons Chris gave

). Speak to a manager or the owner. Show them a copy of the newsletter and explain that you're wanting to distribute them for free into their business. Explain how it'll be a win/win situation where they pay nothing, the customers will have some light reading/jokes, and you'll clean up/replace them each week.
Just keep a simple log of the business name, address, and name of the person who approved it (for future reference).