In antiquity, specifically, theaters back in the ancient rome & greece, the problem of lighting was solved by building theaters as outdoor stadiums (as I am sure you have seen), with most activity occurring during the day light hours. Theaters were usually built & oriented to maximize natural light.
In the 13th AD century you see the emergence of rough lighting 'devices'. An excerpt from the Edison book below also notes that "Cressets, or crudely woven baskets of iron, mounted on poles, were filled with blazing pine knots and pitch, and by their fitful, flickering glare the audience viewed the tableaux and religious spectacles being staged. "
16th&17th Century saw the emergence & integration of candlelight into the theater. Theaters still, however, were regularly built as open air arenas nevertheless, so as to maximize use of daylight when available. You also had, in this time period, the appearance of colored lighting, by masking candles with glasses of colored water.
18th Century saw the birth of the Oil Lamp
19th century saw the emergence of gas lighting, which premiered on stage in 1815 at the London Lyceum.
And late 19th C+ saw the birth & emergence of electricity.
There is an abundance of resources available online that you can access and read, and I've listed a few that all look at the topics above.
The History of Stage and Theater Lighting By the Edison Electric Illuminating Company
Prior to 1804 your choices were basically limited to sunlight or candles/lamps. Lots and lots of candles. The Sam Wannamaker Playhouse in London was designed to recreate the experience of candle-lit indoor theater circa 1600. Dr Farah Karim-Cooper, Head of Research, and Paul Russell, Production Manager discuss the use of candle lighting in performance at the Wannamaker in this video.
In 1804 gas lighting is demonstrated for the first time at the Lyceum Theatre in London. By the 1850s, gas lighting in theatres had spread practically all over the United States and Europe. Gas had many advantages when it came to lighting a set, but it consumed lots of oxygen and could produce uncomfortable amounts of heat. In the 1880s as cheap incandescent bulbs became available, theatre owners rapidly electric lighting.
A great book on the subject is Theatre Lighting Before Electricity by Frederick Penzel, 1978.