The LDS church does not have a subscribable newsletter, but it does offer magazine subscriptions. LDS magazine subscriptions are available for purchase and renewal at the church's online store, store.LDS.org. As of May 2015, the magazine subscription renewal link is located to the left of the main LDS store webpage.
To renew a current or previous subscription, log in using your LDS account user name and password. Enter the previous subscription number as it is written next to the recipient address on the back of an old magazine, and then select the number of years you wish to renew the subscription for, add it to your cart and pay and check out. If you received a renewal notice in the mail, alternatively fill out that form and mail in your payment to renew the subscription by mail instead of online.