Note 1: People are sometimes confused by the fact that there are multiple Lemmy websites like lemmy.world and sh.itjust.works - don't worry about that. Just sign up on one site, and you'll be able to join and interact with communities on any other Lemmy site. Choosing which Lemmy site to sign up to is a bit like choosing your email provider - e.g. if you use gmail, you can still communicate with people who use other email services like yahoo or protonmail. The reason there are multiple sites is because anyone can create their own Lemmy instance - so no single person or company controls the 'fediverse'. Just choose a popular and reputable one like lemmy.world.
Note 2: You can use lemmyverse.net to help you find communities across the whole fediverse. If you've signed up to lemmy.world, then you can visit 'local' communities like lemmy.world/c/memes - and if you want to subscribe to or interact with a community on a different site, then just add @SiteName to the end of the community URL. For example, if you're signed up to lemmy.world, but you prefer the lemmy.ml memes community, then you can visit lemmy.world/c/memes@lemmy.ml to subscribe to and interact with the lemmy.ml memes community.
Note 3: Lemmy is based on the same technology as Mastodon. Both services "speak the same language" (that language is called 'ActivityPub'), so you can view and interact with Mastodon content from Lemmy, and vice versa. They're both part of the 'fediverse', but Lemmy provides a Reddit-like experience, whereas Mastodon is more like Twitter.
Note 4: It's worth mentioning that Lemmy is young - the Lemmy devs are working hard to quickly improve the software, and server admins have been constantly moving to larger machines to support the influx of new users, so please be patient with bugs and issues. Also, the only way to grow Lemmy is for people like you to spend time on the site daily, interact, create new communities, etc. - please join us on this new adventure :)