First of all, there is no correct way of riding a bike, but there is a proper position for you. The way you ride your bike depends on you, on your body frame, your style of riding so you will be the one to choose what is the best position for you, but there are some excellent parameters for you to follow to check which will work best for you.
When you sit on your bike, the best saddle height is when your leg is not on a full stretch. Your leg should have a slight bend of around 25 degrees when the pedal is at the bottom of the stroke. Less than this and you are not using your leg muscles to operate at the most efficient way, more than that will create tension to your legs.
Your knee position is also vital to get the best riding position for you, Hold the pedal in a horizontal place to check this; there should be a plumb line from the center of the knee right above or slightly behind the crankarm.
Measure the distance from your shoulders to the top brake levers when the rider is sitting on a more upright position then that is the reach. The best and most comfortable position is when the rider sits on an angle of 45 degrees from the perpendicular of the bike. This way, you are not crouching too low or stiffly upright.
Bike handlebars are shaped to give the rider three positions where they can comfortably grip - the tops, hoods and drops.
Tops - these are quite literally as they sound the top straight portion of the handlebars.
Hoods - the hands grip the brake lever hoods at the top of the curved portion of the handlebars.
Drops - the hands hold lower down the curve on the dropped or curved section of the handlebars.
Referring to the "reach" choose whichever way is the most comfortable for you. Just like the saddle height, your hand reach is best if you a have a little bend in your elbow, so avoid tension. It is also a good practice to vary your handling position from time to time to prevent numbness and allow more circulation in your arms during your rides.
Pedal Foot Position
Generally speaking, the ball of your feet should be on top of the pedal, but then again, it depends on your comfortability. Some want it to be positioned more in front of the foot for more control. Be mindful that if you are in a wrong position, you may be at risk of injury. Incorrect positioning can force the leg into an unnatural twist, reducing the performance and increasing the risk of a knee injury.
Lastly, your comfort should be your goal when it comes to proper body positioning when riding your bicycle. So get on your bike, test, and adjust according to your body frame, according to your movement.
Try out a few positions. But always remember, only you can say which position is the best position for you.