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.
IMHO, selecting an instance is definitely the biggest user experience problem Lemmy has at the moment. New users who are unfamiliar with the platform are going to pick the biggest instances, and that's going to create performance problems.
We'll need to prioritize work on instance browsing. Lemmy has outgrown the experience over at join-lemmy.org. If I could wave a magic wand, instance browsing and onboarding would have a way to show instance capacity / performance, a way to categorize and filter instances, and a way to recommend instances based upon interests. That would probably help to spread people out more evenly.
There's a website I highly recommend called fediverse observer, it doesn't really go based on interest, but it has some other factors it uses and I really like it.