This can be a difficult skill for many people. Most people prefer to do either one or the other. Even if you can sing and play, it is hard to put them together. My recommendation is to learn to play the guitar, strumming while singing is probably where you want to start and practice makes perfect. Do this every day and it will become more natural.
An the other hand, the piano can be a little more tricky. The best thing to do is play the chords on your right hand and use the left hand for the base is you plan to sing while playing the piano or keyboard. I find this the easiest method. Playing the chords with the left hand while playing melodies with the right hand and singing at the same time is very difficult.