Most waves occur because of wind, and wind is caused by fluctuations in air temperature. Wind on calm water has little grip, but as soon as there is a disturbance, the wind can get a grip on the water and cause it to rise in a circular motion. Wave height depends on many things, including water depth, wind speed and the angle of the beach slope. Generally, waves get higher closer to shore because they slow down. This makes the crests become longer and troughs lengthen, but the amount of change increases according to the beach slope and other factors.
Tsunamis are large, dangerous waves caused by earthquakes on the ocean floor. Earthquakes that cause tsunamis are generally of a magnitude 7 or greater, and in relatively shallow seas less than 30 km deep. Tsunamis are different from wind-generated waves. There is no circular shape to them, just a flat wall of water. There is also an accompanying roaring sound to the tsunami which is very distinct. A tsunami wave can strike quickly and kill many, which happened when tsunamis struck Japan after the March 11, 2011 earthquakes, and more than 25,000 people were killed.
A storm surge is the result of water being pushed to shore by a hurricane or tropical storm. It is not to be confused with storm tide, which is the storm surge added to the normal tide. Storm surge is often the most dangerous part of a hurricane or tropical storm, rising 20 feet or more above sea level. Hurricane Katrina's storm surge was over 25 feet.
If you want to learn about how ocean waves occur, you can do a simple experiment with a flat pan, water, a fan, and some marbles. Fill the pan about halfway with water, and point the fan at the water and put it on low. Notice what happens to the water. After a trial with wind and water, add the marbles and do it again, with the fan at the same speed. The marbles will show the transfer of energy through the waves.