Probably the best way to learn it - to learn some “easy” songs
As you can guess, when you use simple downbeat pattern, you can easily talk a little bit, maybe sing, because downbeat are easy for brain automation
But when you begin to use up beats or off beats - you begin to stuck and hate yourself. You can’t count difficult lines authomatically
Second problem is what you sing not automatically…
When you trying to sing and play at the same time, you use your brain for one of them. It means what you alternating between two processes
Solvation is to get half of the guitar playing process automatically, and for vocal line - same, get some easy moments and train your brain to do it automatically
And third problem is synchronization between them. Because if you will sing faster than guitar like twicely, you will be looking like a “rock rapper”
So, there’s some really “easy” songs which are perfect for getting this skill
Come as you are - Nirvana (because it’s syncopated riffs)
TNT - AC/DC (off bit here)
Highway to hell - AC/DC (off bit again)
Through the never - Metallica (it’s downbeats here but they’re fast, really fast)
Rusty Cage - Soundgarden (it’s one of the hardest songs for singing and playing at the same time, because a lot of time signatures and changes, but if you get it, I guarantee what you will increase your skill)
One cool stuff what in these songs hardest stuff is to play alternate picking stuff with singing, or it’s the off bit stuff, which is hard to count and staying groovy
By the way, these songs are amazing and cool, but only for my opinion, so check them all
P. S. Don’t hate me, all my language mistakes here because I’m not native English speaker, just learning language, so, wish me luck 