"Far away" is always relative. Astronomically, earth/moon are incredibly close, the solar system is tiny, but our entire galaxy is still bound together by gravity.

Earth/moon are about 248,000 miles, centre to centre. The earth has a radius around 4000 miles. Gravity is an inverse-square law (one of Newtons, where f = G * m1 * m2 / ( d * d).

Water on earth nearest the moon is at about 244 thousand miles, and water furthest from the moon is at about 252 thousand miles. The relative pull is 252 * 252 / (244 * 244), which is about 1.07. That is a difference of 7%, which is really not trivial.

Actually, the mechanics don't work exactly like that. Earth/moon behave slightly like a binary star system - they rotate round a common centre (although the earth dominates so much the joint centre is still below the surface). However, the tide nearest the moon is mainly pulled up by gravity, but the tide away from the moon is mainly the centrifugal effect because it is further from the centre of rotation.

Tides are also heavily affected by the land boundaries of the oceans and seas. If the time it takes the water to slop back and forth is close to any harmonic frequency of 24 hours, each day's tides reinforce the pattern until the energy losses match the daily input from gravitational attraction.