The stuff you're playing has to be really tight so that you don't even have to think about - your hands can be trusted to just do it. Just practice practice practice - if it is a written piece. Chords are usually easy because you only need to get a few shapes/movements tight, and they are usually rhythmic so you don't have to focus on multiple rhythms that may/may not be related.

If you are completely improvising just make sure you have lots of licks and practice practice practice those so they are tight, and let your hands do what they want. It pays not to practice doing both simultaneously right away, especially if you're a beginner - but rather to make sure your guitar is tight and thoughtless and then focus on doing the singing over it once it is.

EDIT: Also most of those players aren't playing at the same time, the blues is good like that you can call and respond with guitar and voice and it sounds great. Partly because that would be real hard, partly because it isn't usually good to have two dominant melodic voices - they clash if you aren't careful.