Justin Bieber began his career by teaching HIMSELF to play 4 instruments, the piano, trumpet, drums, and guitar. He entered local contests and performed as often as he could. The first step to sing like Justin Bieber is to perform as often as possible in front of others. Any fears you have about singing will be overcome by the fact that you have to put on the show!
The second step and the first step to actually getting the technique of singing like Justin Bieber down is to realize that the vocal chords, all the way up to the tonque, are muscles that can be strengthened just like your bicep!
Grab a piano and start with a middle C. Tune your voice to the note and sing it. Go as far up and as far down as you can. Do this warmup before every practice. Every practice, push yourself to go that one note farther up and down, just like if you were weightlifting!
As you increase your vocal range, you also want to control it. A large range is no good if you can't hit the note you want to hit! You train controlling your voice by singing arpeggios. If you don't know what those are, they are just the notes of a chord played one at a time. There are many videos on Youtube that can tell you what keys to press on a piano if you don't have someone who can do it for you.
The last step to singing like Justin Bieber is to practice mimicking songs that you know exactly. If you can match notes, you will soon learn how to harmonize and eventually, you can start singing your own songs like Justin!
Youtube has many songs you can practice on. Sometimes you can't tell if you're singing quite right, so ask your parents or friends to critique you until your ear develops!