The bit that makes sense – tidal forces
My physics teacher explained that most tidal effect is caused by the Moon rotating around the Earth, and some also by the Sun.
They said that in the Earth - Moon system, the bodies are in free-fall about each other. But that points on the surface of Earth, not being at Earth's centre of gravity, experience slightly different pulls towards the Moon.
The pull is a little greater if they are on the Moon's side, and a little less on the side away from the Moon. Once free-fall is removed, on the Moon side this feels like a pull towards the Moon and on the the opposite side it feels like a repulsion from the Moon.
This makes sense to me, and is backed up by other questions and answers here, like this and also this Phys.SE question.
The bit that doesn't make sense – tidal bulges
They also said that there are "tidal bulges" on opposite sides of the Earth caused by these forces. The bulges are stationary relative to the Moon, and the Earth rotating through the bulges explains why we get two tides a day. They drew a picture like this one…
An image search for tidal bulges finds hundreds of similar examples, and here's an animation from a scientist on Twitter.
…But, if there is a tidal bulge on both sides of Earth, like a big wave with two peaks going round and around, how can an island, like Great Britain where I live, simultaneously have a high tide on one side and a low tide on the other?
For example:
- Holyhead tide times on the West coast
- Whitby tide times on the East
Two ports with tides 6 hours, or 180º apart. It's high tide at one while low tide at the other. But they are only 240 miles distant by road.
Great Britain is much smaller than Earth. It's probably not even as big as the letter "A" in the word "TIDAL" in that picture.
To prove this isn't just Britain being a crazy anomaly, here is another example from New Zealand:
Two ports that are 180º (6 hours) apart, but separated by just 200 delightful miles through a national park. New Zealand, unlike the UK, is in fairly open ocean.