I have heard about the weekly newsletter. How do I subscribe?
You can get at newsletter subscriptions three different ways.
User Edit Page
Click on your username at the top of the page to go to your user profile page. From there, click Edit to see the option to subscribe to the current site's newsletter.
Master StackExchange list
Via your Network Profile page, you can click on Newsletters.
That will take you to the Newsletters page where you can see all the possible newsletters, and to which ones you subscribe.
Sometimes, the adverts on the sidebar on the right of the question pages will show an advert that can be clicked on.
[Hat tip to @KevinMontrose for his answer to a similar question.]
Here is a page where you can get list of all sites you can subscribe to