There's no magic bullet for learning how to play ukulele and sing at the same time. You need to coordinate your left hand for chord transitions, your right for strumming, and your voice for the melody. This takes a lot of practice.

Make sure you're playing and singing in the same key. This requires finding the starting note for singing the song. Eventually, you’ll be able to do so by ear - after playing a few chords in the song, you’ll just “know” what to sing. However, if you can’t do this yet, try matching a recording.

Here are some tips:

• Practice one component at a time.
  • Left hand - chord transitions. Keep the strum pattern simple, and focus on transitioning chords at the right time.
  • Right hand - strumming. Mute the strings with your left hand, and focus on the rhythm.
• Play along with a Youtube video. You can slow it down to 0.5 speed. Here are some recommendations for ukulele play-throughs with vocals and ukulele accompaniment.
  • I post covers and link song chords.
  • Cynthia Lin makes ukulele tutorials.
  • Ukulele Underground makes ukulele play-throughs with the chords on the screen.
  • GuitarZero2Hero makes play-throughs. He plays guitar, but you can just look up the ukulele chords.
• Kinda sing. Try singing only a couple of words while playing ukulele. Hum the song.