In my experience with the guitar, I think I do best with strumming. But it's always difficult for me when I have try to keep singing while strumming. How can I learn to do both?
@Mark is right on. You've gotta practice enough so you can do it without thinking, even without the instrument.
My trick for getting there… play and read the news at the same time. It takes practice; at first you'll only be able to read a headline and then you'll mess up a chord, but eventually you can digest entire news stories while you're playing through a song. That way you don't have to actively think about DOING something while your muscles are going through the strumming and chords to a song.
I've heard of people who play in pit orchestras for broadway, etc., being able to read books while they play. Could be a rumor… but if you play eight shows a week for a year, I bet you get close to that!
If you have to do 2 or 3 things at a time, make sure you have to think about only one of them. So, in this case, really practice the guitar part until it goes automatically. Then, start to rehearse it together with the singing. Good luck!
Try to keep the strumming simple with one strum per four beats then as you get comfortable strum once every 2 beats. Progress to one strum per beat, eighth notes to sixteenth notes while singing the lyrics.
I have tried singing while playing guitar before and the only answer I have got to this question is: start at a slower tempo to the song that you are practicing, then slowly get faster and faster until you can sing and play at the right speed. It might take a while but it's worth it. Good luck.