The direction in which the celestial bodies are located is seen directly in the telescopes (two angular coordinates); the distance from the Earth is the hard part. For planets, we may measure the distance by waiting for a radar echo.
Aristarchus has invented a useful method to get a third piece of information: when the Moon is exactly half-full, Sun-Moon-Earth form a right angle with the Moon angle being 90 degrees.
The distance from the Earth to the Sun has also been measured by the transit-of-Venus method - to measure the time it takes to cross the Sun. Another method is parallax - measuring and comparing the apparent locations of the celestial objects at the same time, as seen from two places on the Earth.
Still, the angular information - 2/3 of the coordinates - is the most accurate one. Tycho Brahe, a royal astronomer in Prague, measured the positions of planets extraordinarily accurately. The fact that he believed the geocentric system couldn't affect his precision. After all, you may describe everything from the Earth's reference frame.
His young assistant Johannes Kepler - who realized that Copernicus' heliocentric model was right - used those accurate data by Brahe to derive his Kepler's laws. Note that even if you don't know how the distance from the Earth is changing as a function of time, Kepler's laws make many very constraining predictions for each moment of time - where the planets and the Sun should be seen. Kepler has simply made the right guess and verified the predictions of this guess.
In Prague, Brahe was afraid that Kepler could try to get rid of him, so that Kepler would become the main royal astronomer himself. At the end, Brahe died because of not-quite-understood problems with the bladder. I don't claim that Kepler poisoned him. ;-)