Since so much of human existence depends on water, how have people survived crossing deserts where there is precious little precipitation?
An oasis comes about because of the availability of fresh water coming from underground reservoirs that are able to supply the surface because oases are at lower elevations than surrounding areas. Some oases use surface water as well from lakes and rivers.
Oases are often below sea level (although what is really important is how the oases surface level compares to the local groundwater table). The availability of groundwater makes the oases fertile so date palms, citrus, and other vegetation can thrive–also providing drinking water for humans and animals. It follows that oases in the Sahara Desert are essential stopping points for caravans; a caravan going North to South through the Sahara must go from oasis to oasis.
Some interesting things about the groundwater: it can be high enough to make pools of water, sometimes it is close enough that deep plant roots can get to it, and occasionally artesian wells can be used to extract the water. If shallow wells do not produce water, however, then a qanat will have to be built (see below). Modern day oases are moving toward the use electric pumps to get water up from deep wells dug using modern mechanical equipment.
To understand how oases use water, consider an artesian well. An artesian well works since water pressure builds with depth; you can get water to flow out of a well if the output of the well is located at a point that is lower than the highest points of the surrounding groundwater (called the water table).
This seems simple enough, but the problem is that the largest supplies of underground water are typically located in the mountains surrounding the oases. This is because the air flowing upward from the alluvial fan will cool and is unable to hold water, therefore there tends to be more clouds and precipitation above the mountains (as mountain travelers are well aware).
Thus the water aquifers are in the wrong spot! But they are also higher because they are in mountains, though underground. In order to get enough water for your oasis, which may be rather large in area, you will need a qanat.