There is no single comprehensive source for American and Canadian newspapers. In some cases you will need to look at one website for current and recent issues of a newspaper e.g. Nexis Advance UK, and at a different website to look at older issues of the same newspaper. Some websites are free, others can be searched for free but require you to pay to read the articles you find, and others require you to take out a subscription to search them.
The following websites to help you find American and Canadian newspapers:
This database offers access to the full text of over 190 Canadian newspapers from Canada's leading publishers. This full text database includes the complete available electronic backfile for most newspapers, providing full access to the articles, columns, editorials and features published in each. Some backfiles date as far back as the late 1970s.
Links to various newspaper archives, arranged via state. Includes both fee paying and free resources.
Listings of Newspaper Archives and Indexes
Contains the U.S. Newspaper Directory which gives publication details of American newspapers published between 1690 and the present, as well as the full text of selected historical newspapers from the period 1836-1922
Pay to use service containing wide range of digitized papers
Despite its name Nexis Advance UK is a worldwide service so includes many North American newspapers: