Oil lamps have existed since ancient times (pre period) and lasted throughout period and nearly all regions of europe and the middle east. Oil lamps are a very efficient, safe and economic way of lighting an area, lasting longer and being easier to produce than candles, for about the same ammount of light. Oil lamps were probably the major source of household and feast hall lighting for most people throughout period, differning only in quality with wealth. Candles were mainly only used by the church and for specific purposes.
Oil lamps must consisit of a vessel which contains some oil, a wick and possibly some device to hold the wick in the correct place. The vessel may be as simple as a shallow bowl or cup, or may be an elaborately shaped vessel (eg aladdin's lamp). It may be made from glass, metal ceramic or stone. The wick is a braid of fibre (eg cotton) which soaks up the oil and burns. The wick can be just draped over the side of the vessel (where it will drip onto the table or floor below unless you place a saucer beneath it) or a special device to hold up the wick can be constructed. Multiple wicks can be used in the sample lamps, the only consequence - your oil runs out quicker.
Many different oils can be used eg castor oil, however, the most availible kind to modern reconstructors is olive oil. Because vegetable oils burn at a much lower temperature than normal fuel oils, oil lamps are much safer than kerosine lamps as if the oil spills it will not burn badly, nor will it set fire to surrounding objects - only the wick is able to set objects alight. Some oil lamps designs are even safer - hanging lamps may be designed to invert their contents over the wick, estinguishing the flame if knocked. Water may also be added to the bottom of a lamp. While the lamp is stable the oil will float on top and travel up he wick. If it is knocked, the water will extringuish all flames and furthermore, the water makes such lamps safe to place upon wooden objects - the water will keep the bottom of the vessel cool and prevent scorching of table surfaces. Unlike fuel lamps, oil lamps can be safely refilled while burning, as the oil cannot ignite from the open flame (it needs the help of the wick to burn).
Oil lamps can sit on a table (beware metal lamps may get hot bases), be held above the table by candelabra (either singly or in groups), or can be hung from convenient objects. Elaborate chandeliers made of many oil lamps were constructed in period.
For instructions on how to make your own oil lamp from easily obtained conponents, see making oil lamps