Its not very hard at all.
This experiment is performed thousands of times a year in highschools all across the country, I'll explain it in laymens terms because its not necessary to drown ourselves in needlessly overcomplicated words and stuff:
With an electrolysis machine, you can force the molecules of water to seperate in their two component elements (this process is called chemical decomposition).
2H<sub>2</sub>O + Energy ---> 2H<sub>2</sub> + O<sub>2</sub>
In one tube of the electrolysis machine is oxygen gas, in the other tube is hydrogen gas.
We can then take each tube and through a few simple tests, you can see that the two gases formed have demonstratably different chemical properties.
Here's an example a test you can perform: Take two jars, one with "normal air", the second with the mystery gas (which is Oxygen), light a match in both of them. The Mystery Gas allows the match to burn twice as long as the Normal Gas jar. The Mysery Gas is named "Oxygen". This proves that air consists of many types of gases, this is why "air" is not an element.
See
this link for a more detailed explanation and a picture of an electrolysis machine.