I'm going to answer your question in two parts: 1) William the Conqueror's own idea of the difficulty of the invasion of England, and 2) the strategic course the invasion took. Now, to address the first part, William knew that invading England would not be a cakewalk. It was a gamble, the single riskiest endeavor the Conqueror ever attempted in his 40 year rule as duke of Normandy including his 20 year rule as king of England. That William understood the inherent risk of the venture is illustrated by his designation of his young son Robert as his heir (and sworn oaths of fealty to by the Norman magnates) in the months leading up to the Conquest and that he left his wife Duchess Matilda and the elderly Roger Beaumont as regents of the duchy in his absence. Duke William took the proper precautions to ensure, as best as he could, the continuation of his line should his invasion fail.

As far as the actual invasion is concerned, I think a timeline would best the Conqueror's overall strategy in seizing the crown of England. William and his host set sail from Normandy on September 27th, 1066. He landed in Pevensey, England on September 28. From Pevensey the Ducal army traveled to Hastings and quickly constructed a castle (a wooden one, but wooden castles were the norm in 11th Century Europe). William chose the site of Hastings because it was an easily defensible position and had a harbor where he could station his ships in the event he needed to make a quick retreat. Also, Hastings (and Pevensey, for that matter) happened to be a part of the earldom of King Harold Godwinson, William's chief rival for the throne of England. William used his position at Hastings to ravage Harold's lands in order to goad him into fighting, for if Harold could not protect his own earldom (in the eyes of the English lords) he was not fit to rule as king. This action by William succeeded in drawing Harold out to fight the Conqueror and forced a decisive battle, exactly what William was looking to do.

Harold's Saxon host met that of William and his army at Senlac Hill, a few miles from Hastings in the early morning of October 14th. The ensuing battle lasted most of the day and the outcome was uncertain for much of its duration. However, as the day wore on Harold's defensive position weakened; the battle was ultimately lost by the English when Harold was killed in combat (tradition says by an arrow through the eye, although he could have been slain by Norman cavalry). The English army routed and Duke William won the decisive battle he was seeking all along. It is here that William made one of his only mistakes during the Conquest. After the battle, William remained at Hastings awaiting the submission of the English nobility; in this miscalculated for upon hearing of the death of Harold, the English named Edgar the Atheling, member of the royal family, as king. For five days William remained at Hastings, waiting in vain for the submission of the Kingdom of England.

On October 20th, he realized he still needed to impress upon the English that he was indeed king and that resistance was futile. On that day he reached the town of Romney, in Kent, and put the town to the sword. Upon hearing the fate of Romney, Dover, the foremost port in southeastern England, surrendered immediately. From there, William marched toward Canterbury, home to the Archbishop of Canterbury, the highest ecclesiastical position in England. At this point, William's advance halted for a period of five weeks due to an outbreak of dysentery. This was not all terrible however, for this pause allowed the English nobility to fully appreciate the magnitude of William's victory at Hastings. During this time, more and more regions of the south of England, the traditional base of royal power, submitted to William the Conqueror. With the surrender of Winchester by the late King Harold's wife Edith, William gained control of the all-important royal treasury. In the south the only city that remained unconquered was London, the capitol. William thus marched in a circuitous route around the city to isolate it. Once that was done, the English nobility finally began to submit to William. He was given hostages and oaths of fealty. On Christmas Day, 1066 William the Conqueror was crowned King of England.

As a side note, William did not march to York during the initial invasion of England in 1066. He chose instead to leave the local earls Edwin and Morcar in charge of the North. It was only after repeated rebellions did William remove these earls and install Normans to rule in their stead, although the North was not pacified until the winter of 1069/1070 when William executed the infamous "harrying of the North" in which he devastated the land, killed the peasants and induced an artificial famine that killed tens of thousands.

I hope you found this answer helpful!

My sources include: William the Conqueror by David C. Douglas, The Norman Conquest a New Introduction of Richard Huscroft, and the Bayeux Tapestry.