Tip 1: Learn the guitar part inside-out
You need to know the guitar part of the song you’re trying to play and sing like the back of your hand. The sooner that playing that song becomes second nature, the sooner you can focus on incorporating your singing.
Just like the driver of a car being able to talk to you while they drive, or sing along to their radio for that matter. Driving is second nature to them, due to all their practice and experience of a repetitive series of actions.
Tip 2: Isolating Difficult Bits
You’ll probably find that some sections of songs are relatively easy to play and sing and come very naturally. Other sections seem to make you stumble again and again. Going wrong in the same place every single time is a very common problem.
The solution is to isolate that bar, or line, or whatever it may be and to break it down. By far the most common reason that a section is tricky is that the rhythm of the guitar part is contrasting with the rhythm of the vocal part.
So break it down and work out some key points or milestones. You might discover it’s difficult because the vocal line begins on the offbeat (the space between beats rather than on a beat itself) or it’s “between strums” rather than at the same time as a strum. Therefore what you do is to use the strum or beat just before the vocal as your cue, and sing in the gap straight afterwards. You use the unusual features to your advantage by turning them into emphasised cues or prompts. Practise the difficult section slowly and in isolation and soon it’ll come as naturally as the easier sections.
Tip 3: Exaggerate The Rhythms
To help rhythms and dynamics become natural, you should exaggerate them slightly during the learning and practising stages.
Playing and singing a song smoothly is generally the aim, but that is an aim of performance not learning. Particularly in a singer/songwriter style, there is nowhere to hide and glossing over things is not an option. I’d suggest that until the song becomes second nature, emphasise strongly any rhythms and dynamics, without worrying if it sounds a little clunky, before reining this back in once you’ve learnt the song properly.
Happy Playing and Singing!