Stand on a beach for a day and the sea rises twice and falls twice. The near-side bulge is easy to explain. The puzzle is the second high tide, on the side of the Earth facing away from the Moon.
Gravity gets weaker with distance. The Moon is about 384,400 km away and the Earth is about 6,371 km in radius, so the ocean directly under the Moon sits roughly 3% closer than the Earth's centre, and the ocean on the far side sits roughly 3% farther. The pull on all three is slightly different.
The Moon's pull on the Earth's centre is tiny, about 0.000033 m/s², a three-hundred-thousandth of everyday gravity. The pull on the near ocean is a little bigger, and on the far ocean a little smaller. Those small differences are the whole story.
The Earth and the Moon orbit a common point, so the Earth is constantly falling toward the Moon, like a space station falling around the Earth. In free fall the shared pull cancels out, and only the differences in pull are left.
Take the Earth's centre as the reference. The near ocean is pulled harder than the centre, so it is stretched toward the Moon. The far ocean is pulled less than the centre, so the centre is pulled away from it and it is left behind: stretched away from the Moon. Along the sides, the Moon's pull points slightly inward and squeezes the water. The result is two bulges and a squeezed ring, not one lump.
Drag the Moon around the Earth. The little arrows show the pull left over after the average is removed. Press play to spin the Earth under the bulges and watch the tide gauge at the "you" dot.
Spin the Earth under the two bulges and you cross a high tide twice per turn. If the Moon stood still, that would be every 12 hours. But the Moon moves on in its orbit, about 12° a day, and the Earth has to turn extra to catch up with it. A full turn relative to the Moon takes about 24 h 50 min, called the lunar day, so each high tide arrives roughly 50 minutes later than the one at the same time yesterday. Half of that gives the gap in the graph above: about 12 h 25 min between highs.
The Sun pulls far harder than the Moon, but it is so far away that the difference in its pull across the Earth is smaller. Tidal strength falls with the cube of distance, so the Sun's tide-raising effect is only about 46% of the Moon's.
At new and full Moon the Sun and Moon line up, their bulges add, and you get spring tides, the biggest ranges. At the quarter Moons they are at right angles, each fills in the other's low, and you get neap tides, the smallest. The name has nothing to do with the season. Try it: drag the Moon to line up with the Sun, on either side, and then to a right angle, and watch the range readout.
In this ideal picture, with water covering the whole Earth, the difference between high and low would only be about half a metre from the Moon alone, and roughly 0.8 m with the Sun helping. Real tides can be much larger because the oceans are not ideal. Continents block the bulges, and each ocean basin sloshes like water in a bath, with its own natural rhythm. The Bay of Fundy in Canada, whose shape suits that rhythm, sees ranges of up to about 16 m. Some coasts get only one high tide a day, and others get two of different heights.
So the Moon doesn't lift the sea like a magnet. It adds a gentle, repeating stretch that the oceans then answer in their own way.