Storm surges are triggered by a combination of two or three mechanisms; the primary factors are wind speed and the geography of the area but a secondary contributory factor is pressure though this is not necessarily as important as is sometimes thought.
Wind creates waves through surface friction and can produce effects ranging from gentle ripples on the surface to waves 14 meters or more high (over 46 feet) for hurricane force winds of 74 miles per hour (mph) or higher. Such wave heights are normally short lived but if the direction is right they can be driven onto coastlines or straight into estuaries and harbors with devastating effects. The really scary thing about the relationship between wind speed and waves is that the effects are not directly proportional, the relationship is very complex but you can approximate wave heights by a simple formula. If you double the wind speed you triple the wave height. So if a wind speed of 5 mph equals a wave height of 0.2 metres, a 10 mph wind speed equals a wave height of 0.6 meters, a 20 mph wind speed equals a wave height of 1.8 meters, a 40 mph wind speed creates waves of 5.4 metres and hurricane force winds of 80 mph can raise wave heights of 16 meters. Its worth noting that those are average wave heights but this demonstrates how sea conditions can deteriorate so quickly and a relatively small rise in wind speeds can cause problems for even experienced sailors.
The second primary factor is geography which can turn wind driven waves which are only a problem for ships and exposed areas of coastline into a storm surge which can threaten major cities miles from the coast. Wind driven waves can be imagined as a large body of water being pushed ahead of a storm system and so long as they have open ocean ahead of them they will remain as merely waves. If this body of water is compressed between two large immovable and impenetrable objects, such as two shorelines, it acts like a funnel causing the wave heights to become even higher. This is often the case with the English Channel and the North Sea off the east coast of the United Kingdom; just down the road from my house actually. A storm system passes Scotland and enters the north sea and wind driven waves push south towards the English channel but as it passes south through the north sea it is compressed between the western shore of Europe and the eastern shore of England causing wave heights to grow even higher. The effect on waves in the North Sea is negligible but can be far more significant as you approach the shallower waters of the English Channel and the Thames estuary. The Thames estuary becomes the river Thames which runs through London and as it becomes shallower and increasingly narrow wave heights can increase significantly.
A combination of wind speed and the compression factor of two coast lines close together, an estuary or a bay can produce a dangerous storm surge on their own but the third factor can turn a dangerous storm surge into a devastating one. Most cyclonic storm systems, including north Easters, tropical storms, thunder storms and hurricanes, are centered on an area of low pressure. The relatively low pressure causes sea level to rise by approximately 1 cm per millibar of pressure drop and can raise sea level in the North Sea by up to 2 metres in extreme cases. Such as storm system is called a cyclonic system because of the cyclone of extremely strong winds that rotates around it. These winds can drive the raised area of sea level against a shore line and generate waves atop of it, as described previously, but hear is were the geography really becomes a factor. As I noted previously geography can be a factor with waves but unless you're in an extremely confined area like an estuary or bay the effect on wind generated waves is negligible, this is not the case with a rise in sea level generated by a low pressure system. A two metre rise in sea level off the coast of Scotland can become a three metre rise by the time it reaches the English Channel and the mouth of the Thames estuary. If wind drives such as body of water into the estuary it can then rise to 4.5 metres or higher and that's before you add the effects of wind driven waves onto the storm surge.
For a storm surge to be truly devastating it needs to combine all three of the above effects but this is far more common than many appreciate, most of the worlds coastal cities are located on estuaries or bays which will naturally compress an incoming storm surge or tsunami and greatly increase their height. The geographical aspect is not always necessary because a hurricane can produce a catastrophic storm surge all by itself by reducing atmospheric pressure enough to rise sea level by up to two metres and generating winds capable of producing wave heights of 16 metres or higher. A final factor guaranteed to make any storm surge worse is if it coincides with high tide or worse a spring high tide when sea levels are already high in the locality.