The needle is very, very sharp.
Think about this.
Doesn't help?
Okay, now imagine that the tip is not cutting you, but simply pushing aside the molecules of your arm. No harm being done, just finding its way through cells and fibers that will move aside as it approaches. Any pain is imaginary, nothing is touching anything of real substance.
Say it time and time again, until you can watch the infinitely fine point slide happily between your component parts, without batting an eyelid.