Describe in general terms how percent composition by mass is obtained by experiment for new compounds. how can this information be calculated for known compounds?

The traditional method was to carefully burn a small sample in a pure oxygen atomosphere. Carefully capture all the gases that are evolved. For example 2.00mg vitamin C may be burned. The Water is captured by a container that has NaOH.. followed by a container of MgClO4.. to capture C02
Weighing the mass before and after the experiments. We get 3.00mg C02 mass increase

3.00mg C02* 12 gramsCarbon/44 grams C02= 0.818 mg Carbon

0.816mg was gained by the Sodium hydroxide..

0.816 mg H20* 2.02gH/18.g H20= 0.0916mg

0.818g /2.00*100= 40.9% Carbon
0.0916/2.00*100= 4.58% Hydrogen

the balance in this case is oxygen..
100%-(40.9%+4.58%)= 54.5%.
Example from Masterton & Slowinski Chemical Principles..

From known compounds you can simply total up the counts of atoms and the GMW of the compound.

Formaldehyde... CH20... GMW = 30.03

12.011/30.03 *100= 40.0% Carbon
(2*1.0079)/30.03 *100= 6.71% Hydrogen
15.999/30.03 =53.3% Oxygen