If the account already exists, you send an email saying something like "Hey, you tried to sign up but you already have an account. If you need to reset your password, follow this link." If the account doesn't already exist, you send the normal "follow this link to confirm your account" email.

From the attacker's point of view all they get told is "Check your email to continue" whether or not the account is already registered, so it doesn't leak this information.

This isn't always suitable – a mail provider like Gmail is an obvious example – but it would work for the vast majority of websites / web applications.

To be honest, I don't really rate username enumeration as a severe problem for most projects – obviously it's a problem if you can determine whether an email address is registered on, e.g. Ashley Madison or similar though. But it's simply not the case that "nobody else acknowledges it as a problem" – it's a very widely used test, even if the severity is usually considered low.