I sing both backup and lead vox while playing guitar - mostly while NOT playing leads, but I do the occasional vox harmony part over a lead. I don't have a great lead vox, so it's mainly harmonies. There's no special sauce involved. I learned as an adult - it's just practice. Simply put - you can do anything you put your mind to, but you have to want it bad enough!
I got there by singing along to the track/song while rehearsing at home, then doing same at band rehearsal(s), and once I got accomplished enough - at a gig!
I recently started play Bass in second band, and having a REALLY TOUGH time playing walking bass lines and singing harmonies. It's a syncopation thing, but watching Sting do it AND play a foot pedal at the same time boggles my mind! Being able to sing and play guitar I assumed that it would be a *no-brainer* while playing bass. Not the case, but I'm a better singer than our lead guitar, so it makes sense for me do the 3rd harmony - along with the lead vox and the girl - and learn to do both!! I'm also having a similar challenge with fairly simply bass lines and syncopated/offset vocals (example: Backing harmonies on Carrie Underwood's "Before He Cheats"). I'll get there, but it will take a LOT more practice on both.
In summary. No magic here. PRACTICE, PRACTICE, PRACTICE!
The older you are, the harder it will be to *get it*, but keep at it and you'll get there.