by and large. the jab is a misunderstood punch. Most people will 'cock' their arm before throwing it, or step forward and then throw it. Or both. This is a mistake, similar to a hurdler who run up to the block, stops, then attempts to hop over: it's just not the right way to go.
The Jab should be lighting fast, with no preparation to warn your opponent. Think of the same motion you use to flick a light switch: simple, pure, and economical. The power of a jab doesn't come from arm thorwing it. it comes from the ensuing body shift, weight readjustment, and contraction of the leg muscles. It travels in a straight line, from your shoulder, to your opponent's nose( or over his eye-thus hopefully producing a cut that will bleed and obscure his vision).
The elbow should never jut out from the body when the Jab is thrown.If you're a left-lead, imagine that you're standing immediately parallel to a way on your left side, and you need to throw the punch. This will align your body with the punch, and ensure proper body adjustment.
Upon completion, the jab should come straight back 'home'(in your fighting position), immediately in front of your chin. This helps dissipate concurrent counter-attacks, and protects you in chaos that can follow an exchange.
Finally, remember to take your feet with you as you punch, especially if you're trying to close the gap from the outside. Overreaching for a jab is a terrible mistake, and can cost you in terms of speed, delivery, balance, and recovery. In a fight, these are costs that you can't afford.