For baroque/classical opera: just like anywhere else at night: Candles! Lots and lots of candles, and candle-based technology with mirrors. Trying to find pictures but failing! This page has a good overview.

The convention of turning down the lights and only having the stage lit is very new in opera, originating with Wagner. Opera houses were the same level of light as you'd enjoy anywhere else in public at night in those days, though pretty dim and smoky. Complaints about the quality of air in opera houses are pretty common in letters. Also, there were no limelights/spotlights on signers. This contemporary artwork gives you a good idea of what the theater looked like back then, although you can't see any chandeliers. (Take particular notice of the men selling wine and oranges, and the boxes in the stage area.) You could even keep a candle in your box with you, if you wanted to read or play cards, which was totally acceptable.

Oh, and the opera houses burned down a LOT. Open flames are dangerous!

edit: A picture of some worth. Imagine this but on fire.

Limelights are an example of good 19th century engineering. Here's a video of the reaction.

They managed to put this technology in nice, comfortable formats, combined with optics. Here's an example from the 1870s, it was used for projections and effects. Quite a big step up from only using candles during the previous centuries.

They used the lighting technology that was available to them- that is, candles, later replaced with gas burners. Obviously, candles don't cast nearly as much light as modern electric lights, so they used them in great number. In some theaters, you can still see a row of projections sticking up from the front of the stage- sometimes hemispherical, sometimes more boxy, sometimes decoratively shaped. These are known as footlights, and would have contained a small flame, the shell around it serving as a reflector. There were also similar devices in the wings.