How do scientists know what earths temperature would be without greenhouse gases?

Answer 1

Sampling trapped gas bubbles in ice cores gives both historical levels of greenhouse gasses and indirectly by various isotope ratios corresponding historical temperatures. By using statistical curve fitting techniques a function of temperature vs. greenhouse gas levels can be determined and thus the temperature for any level calculated.

An alternate technique is to use computer atmospheric modeling on supercomputers. These models are similar to weather models but usually with a courser mesh to do global temperature modeling instead of detailed local weather system modeling.

There will be uncertainty with either technique, but they agree quite well in general.

Answer 2

They calculate this temperature from Earth's reflectivity and distance from the Sun

Aside from the greenhouse effect, the only factors that affect a planet's average temperature are its reflectivity and distance from the Sun. Since both distance and reflectivity have been measured, the expected temperature can be calculated easily and precisely. (Note that this assumes that the Sun's total emission of energy remains steady; measurements and theory both indicate that it varies very little over time scales less than a few million years.)