The front crawl or forward crawl is a swimming stroke usually regarded as the fastest of the four front primary strokes.  As such, the front crawl stroke is nearly universally used during a freestyle swimming competition, hence freestyle is used interchangeably with the front crawl.

There are multiple ways to start - diving, or from a pool wall, but at the start, the body should be as linear and flat in the water as possible.  The head should be slightly raised but not out of the water, which will cause the body to sink.  If the head is too low, that will cause drag and an awkward motion when it's time to breathe.

Arm Cycle

The arm movements in the front crawl are very important because they are the main source of momentum and propulsion through the water.  To start, one hand is held flat with the palm turned away from the swimmer. The next step is ‘catching the water’.  This is done by lowering the hand into the water thumb first.  Now pull the hand back in a circular movement from the water and back to the chest. Keep in mind the hand and arm should be straight. Now pull the arm backward under both the water and the body to the beginning position.  Each arm should alternate with this process.  This pull and push is also known as the S-curve.   This diagram depicts the arm motion:

Kicking

Kick your legs in a quick, up-and-down flutter motion, while your arms are pulling and pushing your body forward.  Bend your knees slightly at the beginning, then kick the foot and lower leg downward.  The flutter kick involves small kicks, not big splashes, and improves stability and levelness in the water.  Try for six kicks per arm cycle.

Breathing

The freestyle breathing technique is usually the most difficult skill for the novice swimmer to learn.  As you move one arm overhead, turn your head to one side until your mouth is clear of the water's surface without lifting your head out of the water.  Your head should rest on your extended arm.  Inhale quickly, taking a breath on one side only - one breath for each complete stroke cycle.  You should breathe on the same side each time, and use the same side every time you swim so the motion becomes habitual.  Exhale while your head is turned face down in the water, so the lungs empty to prepare for the next breath.

Video

This video brings all the above together.

Sources:

• http://quinnmeyer.blogspot.com/2014/03/picture-blog-swimming.html
• http://www.livestrong.com/article/187074-front-crawl-stroke-technique/
• https://www.youtube.com/watch?v=ioFydzeYgt8
• https://seattleswim.wordpress.com/2012/02/09/swim-tip-freestyle-flutter-kick/
• https://en.wikipedia.org/wiki/Front_crawl