As a small investor, I don't worry about what exchange a particular stock is on.
I created an account with an online broker -- TD Ameritrade in my case, but there are many others out there, and I can't recommend one over another. Then if I'm interested in a stock, I look it up on their website. If they list it, than I can buy it. There are probably stocks in the world not listed on TD Ameritrade. I've had times when I've thought about investing in a particular company and couldn't find it. Maybe that means they're not a public company, maybe I don't have the formal name or they're really owned by a holding company or some such, or maybe they're just not on an exchange that my broker deals with. In any case, I don't worry about it.
If I do find the stock on the broker's web site, than they give me a fair amount of information about it: the latest price of course, what the price has been for the past several years, the last dividend if any, ratings by several well known investment advisory companies, etc. If I want to know more I usually just google the company name and see what else I can find out about it.