Now imagine two people, one in Singapore and one in Bogota, Columbia. These two people are essentially on opposite sides of the earth. If they were to look at the center of the moon, they would be looking in slightly different directions. Their lines of sight, which are also the lines along which gravity acts on the earth from the moon, would cross at the moon's center. So the pull of the moon on the earth due to gravity has a bit of a compressing effect along a line perpendicular to the line connecting the center of the moon to the center of the earth.
That part of the earth that is solid is not much affected by this small compressive force. The liquid part however tends to flow away from the squeeze points and bunch up directly under and opposite the moon. This effect is aggravated by the fact that the gravitational effect of the moon decreases with distance so that near water is attracted more strongly than the whole earth average and far water less strongly. Now as the earth rotates on its axis, it rolls under these two high and two low spots in the oceans so that the water level at any particular point on the earth goes through a peak and valley twice a day.
Of course the sun has a similar effect but smaller because of the greater distance to the sun. When the sun and the moon line up either in a full moon or new moon their tidal effects add, giving larger than average tide swings. When they are most out of line, their tidal effects subtract, giving smaller than average tide swings.