You can sign up here: https://mastodon.social/about
(Solving the "critical mass of users" problem is left as an exercise to the user.)
I think Twitter is easier for the mass public to join. Go to Twitter.com, put username and password, verify phone number. Done! The screens are cleaner and very intuitive.
For mastodon, there's more text and messaging about the differences regarding Twitter, what's the Fediverse, instance rules. So you just landed on the main screen and you have to think about choosing an instance with different number of people, different rules.
After you are in, you can't search!! You can only search usernames or hashtags, but that is REALLY cumbersome and ineffective since people don't write "This is my #Twilight #book #review #bookreview URL". If you are not tech/privacy focused, the trending tags are usually not interesting, apart from #caturday I guess?.
Even after you are able to follow people, you can't quote-retweet (which is a pro AND a con), and even "retweeting" is cumbersome if you are on someone's profile from another instance.
Sharing is also more cumbersome since there's no bookmarklet or chrome extension that I could find, and sites don't have a "share on mastodon" link. The solution was to enable a cross-poster, so I just keep posting on Twitter.
About instances: on some main instances, speed is ok, but try to follow some pic focused profiles on smaller instances. It can take like 5~10 seconds for an image to load. And now on the iPhone official app, I can't seem to be able to download pictures anymore, and the option to bookmark a post (not like) is not there, only on the web-mobile version.
To answer "How to solve that problem?", I'd say don't worry a damn thing about Joe Public.