Noble gases are chemically neutral. They don't react with anything.
So, how were they discovered?
First of all, this is not true that noble gases do not form any compounds -- it can be done with some chemical tricks, usually using fluorine and some hell conditions.
Yet, you don't need any chemistry to detect a new element -- helium was for instance first spotted in the sunlight spectrum. The isolation can also be made by physical means only; the most efficient idea is to cool down air isolating each new fraction that turns into liquid, but there are dozens of other.
The history is summed up in http://en.wikipedia.org/wiki/Noble_gas#History . The concept of noble gas emerged from the discovery of argon.
As said by mpq, the first to be seen spectroscopically was Helium. Then Argon was detected as a component of the air less reactive than nitrogen (http://en.wikipedia.org/wiki/Argon#History ).