I quite like the UX newsletter, and I'd like to share it with other people. But it's really awkward that there's no URL I can direct them to. I have to tell them to sign up to UX, then go to the "manage subscriptions page", search for UX, then subscribe.
This is, ironically enough, a pretty terrible UX.
Ideally, you could go to https://stackexchange.com/newsletters/ux, see the most recent newsletter, [un]subscribe, and get an RSS feed.
There actually is a slightly better way to direct people to sign up for a site's newsletter.
If you direct them to https://stackexchange.com/newsletters, all of the sites are listed, and they'll have the ability to subscribe to any number of newsletters. From that page, the person can either log in/sign up for the site they're interested in, OR they can enter an email address to receive the newsletters without signing up. Basically, it's what you're already telling them to do, but they don't have to sign up for UX first and visit two totally different parts of stackexchange.com. Going directly to the newsletter subscription page eliminates a little extra work and confusion.
Click the "subscribe" button next to the site whose newsletter you want.
Then enter the email address you'd like the newsletter sent to.
If you click the "preview" link under the "subscribe" link, you can see a sample newsletter, though we don't currently have an online archive of all newsletters for a site.
You're right that it would be better UX to have a single, simple URL to direct people to that fits into an individual site's hierarchy. As Anna pointed out, doing something along those lines is on our list, but it unfortunately is lower priority than some other projects we're currently working on.
ux.stackexchange.com/newsletters.site/newsletter? Seems easy to me - but I've never done anything at this scale :)