This site is currently struggling to handle the amount of new users. I have already upgraded the server, but it will go down regardless if half of Reddit tries to join.
However Lemmy is federated software, meaning you can interact seamlessly with communities on other instances like beehaw.org or lemmy.one. The documentation explains in more detail how this works. Use the instance list to find one where you can register. Then use the Community Browser to find interesting communities. Paste the community url into the search field to follow it.
You can help other Reddit refugees by inviting them to the same Lemmy instance where you joined. This way we can spread the load across many different servers. And users with similar interests will end up together on the same instances. Others on the same instance can also automatically see posts from all the communities that you follow.
Edit: If you moderate a large subreddit, do not link your users directly to lemmy.ml in your announcements. That way the server will only go down sooner.
Can attest: I have a small VPS (docean's lowest tier, in fact) and in the deep past I had occasions where a blog post was popular enough to throw it offline for a while. I wasn't about to lock myself into paying more money forever, to keep the site running for a day's peak traffic.
In the case of lemmy.ml, this isn't helped by the frontend being Websockets-driven, which holds open a connection for every concurrent user; I hear Dessalines and crew are working on cutting that dependency out and dropping down to something more static, which should help with load.
The backend actually supports both websockets and REST calls. For instant updates, however, you need either websockets or SSE, which leave an open connection for each concurrent user. I believe there isn't quite any other way besides regular HTTP polling.