There are numerous way in which to carry out parallel parking. Below are details of how I teach it, but, please only use it as a guide and consult your instructor for more guidance.
First of all we need to make sure its safe, legal and convenient. Once we are satisfied that its a suitable location, we need to drive along side the target vehicle, about 1 meter from its side (a doors width) until we are just past the front of it. At this point we select reverse gear and carry out full all round observations starting at our right shoulder. We then end up looking out the rear window as in the picture.
Now slowly reverse back to your turning point. This is usually when the rear seat lines up with the rear of the target vehicle, (all cars will differ, so ask your instructor) as can be seen in picture below. Be sure to check all round for other road users as you reverse back.
At this point, carry out full all round observations, then as we reverse back apply full left hand lock. Keep looking round for other road users. We're aiming to get the car pointing at a certain angle. I tend to use a clock face example for this. If you visualise a clock face, we start at 12 o' clock, as we reverse in we're looking to get the car pointing to between 1 and 2 o' clock as in the picture
Once at this angle, we need to straighten up the wheels as we reverse back towards the kerb. The distance you reverse back will depend on your car. Your instructor will help you with this. On my car, this tends to be when the rear door handle appears to be resting on top of the kerb. You should be able to see this in your left door mirror
At this point, apply full right hand lock on the steering. This will allow the front of the car to swing round into the space. As the car becomes parallel with pavement, quickly straighten the steering. You have now got the car parked.
The main things to remember when doing parallel parking are, slow car, brisk steering and plenty of observations for other road users. Try to keep looking mainly in the direction of travel.
With practice you'll soon become confident in carrying out this exercise.
Below is a video of me explaining, and carrying out a parallel park.