Singing along while you or someone else plays ukulele is a wonderful thing to do.
Lets face it, singing is a wonderful thing to do whether anyone's playing along or not! Some people do it naturally, many develop their skills with a few pointers and we all need a dose of confidence along the way.
Singing is one of my favourite things to do and here are some tips based on what I've learned from many years of variously being in choirs, singing in noisy rock bands with no way of hearing myself, to moments of truth in solo gigs and wonderfully satisfying harmony work in duos, trios, and ukestras.
Things to remember when you're singing:
It's a whole body experience! Posture, breath, bringing your facial mucles into play and engaging your abdominals to support your diaphragm (the muscle that sits under the lungs) are actions that contribute to your pitch control, phrasing and projection.
Especially good to think about when...you're slumped like a hunchback trying to read a chord and lyric sheet while playing a song...and oh, singing it.
Sometimes it's good to stop playing, stand up straight, take in a deep breath through the nose without lifting your shoulders (thereby expanding the lungs and contracting your diaphragm), followed by a controlled outbreath. Do the breath three times. Then sing the song confidently to your audience of devoted fans (real or imaginary), without playing the uke.
After that, you might decide to learn the song off by heart so you can play and sing with greater freedom, OR you'll perfect the glancing-at-the-page-while-standing-up-straight technique which will allow much better voice projection and control.