Here are some examples:
* The Renaissance was a period of great cultural and artistic flourishing.
* Michelangelo was a prominent artist of the Renaissance.
* Leonardo da Vinci embodied the spirit of Renaissance humanism.
However, you wouldn't capitalize "renaissance" when referring to a general revival or rebirth, such as:
* The renaissance of classical music in the 20th century.
* There was a renaissance of interest in poetry after the war.
In short, if you're talking about the specific historical period in Italy, then you capitalize it. If you're talking about a general concept, then you don't.